The letter does indeed carry teaching authority. It is referenced in the Vatican II documents Lumen Gentium and Gaudium et Spes. Vatican II almost word-for-word reproduces this letter’s wording on the salvation of those baptised by implicit desire. An ecumenical council would not give such direct weight to a letter without doctrinal authority.
In the Letter itself we find this:
“…Accordingly, [size=]the Most Eminent and Most Reverend Cardinals of this Supreme Congregation, in a plenary session held on Wednesday, July 27, 1949, decreed, and the august Pontiff in an audience on the following Thursday, July 28, 1949, deigned to give his approval, that the following explanations pertinent to the doctrine, and also that invitations and exhortations relevant to discipline be given:
We are bound by divine and Catholic faith to believe all those things which are contained in the word of God, whether it be Scripture or Tradition, and are proposed by the Church to be believed as divinely revealed, not only through solemn judgment but also through the ordinary and universal teaching office…”[/size]
As Msgr. Fenton in his book, The Catholic Church and Salvation describes as to the meaning of that paragraph,
“We are dealing, then, with an authoritative document. It would be wrong for any teacher of Catholic doctrine to ignore or to contradict the teachings contained in this Holy Office letter.”
Some background info on the Letter:
It is a letter from the Holy Office to Richard J. Cushing who was then the Archbishop of Boston. Here, this “Supreme Sacred Congregation” (the “Holy Office”) specifically states that they have “followed very attentively the rise and course” of the St. Benedict’s Center and their peculiar interpretation of “No Salvation Outside the Church.” So this is no mere , no hasty opinion a long thought out conclusion, for which the Holy Office here has taken full responsibility. This is a situation that the Holy Office had been monitoring for quite some time.
As Griff Ruby explains:
“…To hear the members of St. Benedict Center, Fr. Feeney himself, his present day successors, the Dimond brothers, and indeed all who deny BOB and BOD, one gets the idea that this letter is “nothing more than a letter from two heretical cardinals of the Holy Office, … to one apostate archbishop in Boston,” as the Treatise describes it. Never mind that one of those “cardinals” (actually not yet a cardinal at that time but then a lesser functionary) happened to be none other than Alfredo Ottaviani, a most staunchly traditional and conservative cardinal indeed, and hardly one to be so easily a party to rank error. Yet we find here in this quote the fact that it was discussed “in a plenary session” which means that all members of the Holy Office were present (and none of them objected? - No, none of them did!). When we claim that this letter was reviewed by the Pope and agreed to by him as to its contents, this is no mere apocryphal story, but what is claimed in the text of the document itself. It makes reference to the standard practice of the Holy Office (as it stood then) that their main meetings were held on Wednesdays and the results reviewed and approved with personal papal approval on the immediate following Thursdays, as this happened here on July 27 (Wednesday) and July 28 (Thursday), 1949. This is no mere formality, nor was it anything exceptional, but merely the Holy Office acting exactly as was par for the course…”
On the 8th of August, 1949, Cardinal Marchetti-Selvaggiani, Secretary of the Holy Office, wrote to the Archbishop of Boston and sent him a Declaration of this Holy Office to be conveyed to Father Feeney, which made clear the sense in which one should understand the doctrine that “There is no salvation outside of the Catholic Church.”
It was not simply “One Bishop to another”. It was one Bishop sending another Bishop a Declaration of the Holy Office in its entirety, and under the full sublimity of its magisterial authority, with the express approval of Pope Pius XII (in a similar way to how Pope John Paul II approved the 2000 document of the Congregation for the Doctrine of the Faith, “Dominus Iesus”).
let me refer you to the introduction adjoining this Letter written by the Archbishop of Boston (Cushing):
"…Given on August 8, 1949 explaining the true sense of the Catholic doctrine that there is no salvation outside the Church.
This important Letter of the Holy Office is introduced by a letter of the Most Reverend Archbishop of Boston (below)
The Supreme Sacred Congregation of the Holy Office has examined again the problem of Father Leonard Feeney and St. Benedict Center. Having studied carefully the publications issued by the Center, and having considered all the circumstances of this case, the Sacred Congregation has ordered me to publish, in its entirety, the letter which the same Congregation sent me on the 8th of August, 1949. [size=]The Supreme Pontiff, His Holiness, Pope Pius XII, has given full approval to this decision. In due obedience, therefore, we publish, in its entirety, the Latin text of the letter as received from the Holy Office with an English translation of the same approved by the Holy See.
Given at Boston, Mass., the 4th day of September, 1952.
Walter J. Furlong, Chancellor
Richard J. Cushing, Archbishop of Boston…"[/size]
As such the Feeney letter is binding on Catholics and was the closing of the Feeneyite heresy for good.
As for its absence from the Vatican website, it is in the references to Lumen Gentium and Gaudium et Spes. No the text is not given on its own fully because its teaching is perfectly represented in these Vatican II documents which nearly verbatim re-write it word-for-word.