Logic continues to elude your heresy-riddled mind.  As I mentioned, the only affirmation that Pius XII approved this comes from none other than Cushing.  It's circular evidence.  We know this letter is authentic because it says it is.

And because the questionable Bishop who requested its creation verifies it

 There have been various ways in which Catholic writers have tended to reduce the teaching on the necessity of the Church for salvation to a meaningless formula. Among them, the following may be regarded as among the most important: 

(1) A few writers, obviously unschooled in sacred theology, have simply rejected the formula itself, and thus completely denied the teaching. The unfortunate Arnold hαɾɾιs Mathew, writing during his days as a Catholic, produced teaching of this sort. He makes this statement in the chapter "Extra Ecclesiam Salus Nulla," in the symposium Ecclesia: The Church of Christ, a work which Matthew himself edited:

Now the further question arises as to how far Catholics are bound to hold that for those outside the Roman Church there is no salvation. Catholics are not bound to hold anything of the kind. [Mathew, in his chapter, "Extra Ecclesiam Salus Nulla," in the symposium, Ecclesia: The Church of Christ, edited by Arnold hαɾɾιs Mathew (London: Burns and Oates, 1906), p. 148.] Fenton

(2) The teaching that the dogma of the necessity of the Church for salvation admits of exceptions is, in the last analysis, a denial of the dogma as it has been stated in the authoritative declarations of the ecclesiastical magisterium and even as it is expressed in the axiom or formula "Extra ecclesiasm nulla salus." It is important to note that such teaching is found in Cardinal Newman's last published study on this subject, a study incorporated into his Letter to the Duke of Norfolk, perhaps the least valuable of all his published works. Because of Newman's great influence in the field of contemporary theological studies, it will be helpful to see how he treated this subject in the Letter. Fenton

(3) Some Catholic authors attempted to explain the dogma of the Church's necessity for the attainment of eternal salvation by saying that the Church is only the ordinary means, and that it is still possible, in extraordinary cases, for a man to attain the Beatific Vision outside the Church. At the same time they resolutely claimed, as Newman had done, that it is a Catholic dogma that there is no salvation outside the Church. Manifestly, according to this explanation, the dogma would be nothing more than a vain formula, something which the very people who accept it as a dogma would be expected to treat, for all practical purposes, as untrue. Ultimately, of course, this explanation coincides with the one offered by Newman in his Letter to the Duke of Norfolk. Fenton