The Church makes the visible-invisible distinction in the Letter of the Holy Office 1949 when it suggests that the baptism of desire excludes the baptism of water.

Where does the Church make a distinction between visible and invisible cases when teaching Baptism of Desire?
If you cannot show us, then you have created a distinction of your own making, and certainly haven't shown that the doctrine is merely theoretical.
Be sure to cite the Magisterial document, Pope, year, and reference.
Lionel:
Where does the Church make a distinction between visible and invisible cases when teaching Baptism of Desire?The Church makes this distinction in the Letter of the Holy Office 1949 when it suggests that the baptism of desire excludes the baptism of water.
It makes this distinction between invisible and visible cases in the Baltimore Catechism (1808) when it places the baptism of desire and blood in the baptism of water section, suggesting that the baptism of desire and blood have the same effect as the baptism of water and these cases are known to us, they are visible.
The distinction is made in two theological papers of the International Theologiocal Commission when it rejects the Feeneyite version of the dogma extra ecclesiam nulla salus.It's influence can be seen in magisterial documents like Redemptoris Missio etc.

It is there when, for example, the Letter of the Holy Office 1949 suggests that the baptism of desire excludes the baptism of water and it is an exception to the traditional, exclusivist interpretation of Fr.Leonard Feeney. So the visible-invisible distinction is made. It means that the baptism of desire is an exception to the Feeneyite version of the dogma since it is visible.It is explicit. It would have to be objectively seen for it to be an exception. It would have to be personally known in specific cases for it to be relevant to the interpretation of extra ecclesiam nulla salus according to Fr.Leonard Feeney.So the beginning  of the visible-invisible distinction was there in 1808 and it became official in 1949 and the error was placed in many places in Vatican Council II (AG 7, LG 14), where the baptism of desire and being saved in invincible ignorance are mentioned, even though they are invisivble cases for us.
They were placed in Vatican Council II along with orthodox passages supporting the dogma extra ecclesiam nulla salus. In other words these cases are explicit for them to be inserted in Vatican Council II with passages which say all need faith and baptism for salvation.
So the understanding in the Church, after the error was, all need to enter the Catholic church with faith and baptism, except for those with the baptism of desire.This was a new doctrine. It included the visible-invisible distinction in a subtle way.

-Lionel Andrades

For Francisco Romero Carrasquillo too deceased are living exceptions to the traditional interpretation of Fr.Leonard Feeney

http://eucharistandmission.blogspot.it/2015/02/for-francisco-romero-carrasquillo-too.html

THE INVISIBLE-VISIBLE DISTINCTION IS MADE IN THE FOLLOWING PARAGRAPHS OF THE LETTER OF THE HOLY OFFICE 1949

The invisible-visible distinction is made the following passage which says  only those who know about the Church and who do not enter cannot be saved, instead of the traditional all who are not members of the Church will not be saved.Being saved in invincible ignorance was an exception to the dogma extra ecclesiam nulla salus for Cardinal Francesco Marchetti Selvaggiani, who issued the Letter(1949).These cases were visible and so they were exceptions. So only those who were not in invincible ignorance, who knew, needed to enter the Church or be damned to Hell.

Therefore, no one will be saved who, knowing the Church to have been divinely established by Christ, nevertheless refuses to submit to the Church or withholds obedience from the Roman Pontiff, the Vicar of Christ on earth.-Letter of the Holy Office 1949

In certain circumstances a person did not need the baptism of water since he could be saved with the baptism of desire which excluded the baptism of water.These cases were known to be relevant.They were visible to be exceptions to the dogma extra ecclesiam nulla salus.

In His infinite mercy God has willed that the effects, necessary for one to be saved, of those helps to salvation which are directed toward man's final end, not by intrinsic necessity, but only by divine institution, can also be obtained in certain circumstances when those helps are used only in desire and longing.    -  Letter of the Holy Office 1949

It is not always required to be incorporated into the Church as a member,it is said, since there are visible exceptions is the understanding.

The same in its own degree must be asserted of the Church, in as far as she is the general help to salvation. Therefore, that one may obtain eternal salvation, it is not always required that he be incorporated into the Church actually as a member, but it is necessary that at least he be united to her by desire and longing..-Letter of the Holy Office 1949

Those united only by implicit desire were relevant to the dogma,since they were visible exceptions.The inference was that cases saved with an implicit desire were known can could be known.

With these wise words he reproves both those who exclude from eternal salvation all united to the Church only by implicit desire,..   - Letter of the Holy Office 1949

From the Housetops did not make the visible-invisible distinction.The St.Benedict Centers members who issued this magazine would not say that the baptism of desire excluded the baptism of water and was salvific.There were no explicit exceptions for them.

From what has been said it is evident that those things which are proposed in the periodical , fascicle 3, as the genuine teaching of the Catholic Church are far from being such and are very harmful both to those within the Church and those without.    - Letter of the Holy Office 1949

The St.Benedict Center refused to say that there was known salvation outside the Church.There were no exceptions to the dogma in their artcile.There were no visible exceptions so the magisterium is criticizing them.

Hence, one cannot understand how the St. Benedict Center can consistently claim to be a Catholic school and wish to be accounted such, and yet not conform to the prescriptions of canons 1381 and 1382 of the Code of Canon Law, and continue to exist as a source of discord and rebellion against ecclesiastical authority and as a source of the disturbance of many consciences.    - Letter of the Holy Office 1949

Fr.Leonard Feeney said there was no salvation outside the Church.There were no exceptions for him.He could not see or meet any one saved without faith and baptism in the Catholic Church.He was critical of the Archbishop of Boston and the Jesuit Superior for saying there was known salvation outside the Catholic Church.

Furthermore, it is beyond understanding how a member of a religious Institute, namely Father Feeney, presents himself as a "Defender of the Faith," and at the same time does not hesitate to attack the catechetical instruction proposed by lawful authorities, and has not even feared to incur grave sanctions threatened by the sacred canons because of his serious violations of his duties as a religious, a priest, and an ordinary member of the Church.   - Letter of the Holy Office 1949

They were spreading theological doctrines, which were traditional and did not suggest that there were visible exceptions to the dogma extra ecclesiam nulla salus.It was not tolerated by the Magisterium in Rome.

Finally, it is in no wise to be tolerated that certain Catholics shall claim for themselves the right to publish a periodical, for the purpose of spreading theological doctrines, without the permission of competent Church authority, called the "" which is prescribed by the sacred canons.   - Letter of the Holy Office 1949

Rome was saying there were exceptions. In other words the baptism of desire referred to visible cases, for them to be exceptions.Rome was teaching an irrationality.

Therefore, let them who in grave peril are ranged against the Church seriously bear in mind that after "Rome has spoken" they cannot be excused even by reasons of good faith. Certainly, their bond and duty of obedience toward the Church is much graver than that of those who as yet are related to the Church "only by an unconscious desire." Let them realize that they are children of the Church, lovingly nourished by her with the milk of doctrine and the sacraments, and hence, having heard the clear voice of their Mother, they cannot be excused from culpable ignorance, and therefore to them apply without any restriction that principle: submission to the Catholic Church and to the Sovereign Pontiff is required as necessary for salvation.   - Letter of the Holy Office 1949  -L.A

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Now see the errors of the International Theological Commission (ITC).

International Theological Commission (ITC)

10. Exclusivist ecclesiocentrism—the fruit of a specific theological system or of a mistaken understanding of the phrase extra ecclesiam nulla salus—is no longer defended by Catholic theologians after the clear statements of Pius XII and Vatican Council II on the possibility of salvation for those who do not belong visibly to the Church (cf, e.g., LG 16; GS 22).-International Theological Commission, Christianity and the World Religions 1997. (1)

http://www.vatican.va/roman_curia/congregations/cfaith/cti_documents/rc_cti_1997_cristianesimo-religioni_en.html

Lionel:

‘Pope Pius XII and Vatican Council II has clearly said that those who do not belong visibly to the Church can be saved.’

To be an exception to the exclusive interpretation of the dogma those who do not belong visibly to the Church would have to be known.

Where does Vatican Council II or Pope Pius state that we know these exceptions personally or that they are explicit exceptions to the dogma?. Pope Benedict and Bishop Gerhard Muller just assumed these cases are known to us and so are exceptions to the literal interpretation of the dogma.

Cardinal Luiz Ladaria, the Secretary of the Congregation for the Doctrine of the Faith,Vatican and Archbishop Augustine Di Noia, Vice President of Ecclesia Dei were also associated with the ITC.

International Theological Commission (ITC)

58. In the face of new problems and situations and of an exclusive interpretation of the adage: “salus extra ecclesiam non est”, the magisterium, in recent times, has articulated a more nuanced understanding as to the manner in which a saving relationship with the Church can be realized. The Allocution of Pope Pius IX, Singulari Quadam (1854) clearly states the issues involved: “It must, of course, be held as a matter of faith that outside the apostolic Roman Church no one can be saved, that the Church is the only ark of salvation, and that whoever does not enter it, will perish in the flood. On the other hand, it must likewise be held as certain that those who live in ignorance of the true religion, if such ignorance be invincible, are not subject to any guilt in this matter before the eyes of the Lord”-The Hope of Salvation for Infants who die without being baptized(2007. International Theological Commission)

http://www.vatican.va/roman_curia/congregations/cfaith/cti_documents/rc_cti_index-doc-pubbl_en.html

Lionel:

The Allocution of Pope PIus IX clearly does not state in the passage cited above that those saved in invincible ignorance are explicitly known and so are exceptions to the dogma which says whoever does not enter into the Church will perish. These exceptional cases are known only to God.The Church Councils and popes knew this. This unfortunately was the error of the Archbishop of Boston Richard Cushing and the Jesuits there.

Pope Benedict XVI and Bishop Gerhard Muller, ITC.

59. The Letter of the Holy Office to the Archbishop of Boston (1949) offers further specifications. “To gain eternal salvation, it is not always required that a person be incorporated in reality (reapse) as a member of the Church, but it is necessary that one belong to it at least in desire and longing (voto et desiderio). It is not always necessary that this desire be explicit as it is with catechumens. When one is invincibly ignorant, God also accepts an implicit desire, so called because it is contained in the good disposition of soul by which a person wants his or her will to be conformed to God’s will”.

Lionel:

Yes in principle a person can be saved with the baptism of desire. In reality, explicitly we do not know any case of a person saved in Heaven with the baptism of desire. So it is not an issue with respect to the dogma extra ecclesiam nulla salus. Implicit desire is irrelevant to the literal interpretation of the dogma.It is not even an issue.

66. In his encyclical Mystici Corporis, Pius XII addresses the question, How are those who attain salvation outside visible communion with the Church related to her? He says that they are oriented to the mystical body of Christ by a yearning and desire of which they are not aware (DS 3821).-Christianity and the World Religions 2007

Lionel:

Yes they can be saved and we do not know who are these cases specifically. So one cannot imply that those saved with the baptism of desire are exceptions to the dogma. They are not.

http://eucharistandmission.blogspot.it/2012/07/pope-benedict-and-bishop-gerhard-muller.html