I would accept the following explanation:
"Well, the Pope is giving that as a supporting reason or explanation, and not intending to define that particular point. As such, it's not within the scope of infallibility."
I do not except the tortured imposition of this definition here with ZERO PROOF. Xavier just made it up to explain it away because he doesn't want it to be true.
It's very clear what the Pope believed.
But then neither Pope Innocent II nor Pope Innocent III was defining either, but merely opining in favor of BoD.
So one Pope did not believe in it, but those two did.
Same thing with the Canon Law question, where the 1917 Code permits burial for catechumens. At the same time, earlier Church discipline forbade the practice.
Same thing with the Fathers. One or perhaps two of them might have believed in BoD ... at least for a time. But 5 or 6 of them explicitly rejected it.
What picture emerges? That BoD is NOT revealed truth, but is in the category of theological speculation, and, as such, it is open to being questioned by Catholics.
But BoDers filter out, ignore, or explain away all of these data points that do not fit their narrative.
What I see is an early Augustine (before he had matured in the faith), saying "having gone back and forth about it, I find [in favor]" but then firmly rejecting it when he realized that it leads to Pelagianism. And I find an ambiguous statement from St. Ambrose that could be understood in one of three different ways ... together with a rejection of the idea that catechumens could be saved without Baptism somewhere elsewhere in his works. Then I see several other Fathers who rejected the idea explicitly. THAT is the Patristic picture, clear and objective, where you can't prove it one way or the other.
Then I see the early scholastics dealing with the question (no mention of it after St. Fulgentius, a disciple of St. Augustine who rejected BoD until Abelard and Hugh of St. Victor). Abelard rejected it but Hugh of St. Victor believed in it. Peter Lombard then sought the opinion of St. Benard for a tie-breaker. St. Bernard opined tentatively in favor, saying that he'd got with St. Ambrose and St. Augustine, "whether in truth or in error." Again, hardly authoritative. Then from Peter Lombard, it got to St. Thomas, and then with St. Thomas it went viral.
Popes Innocent II and Innocent III also opined in favor of it, based "on the authority of Augustine and Ambrose" (a false premise since St. Augustine actually rejected it fiercely and St. Ambrose may have only obliquely referred to the possibility rather than teach it with any authority). So now a tentative speculation from St. Augustine, which he later rejected, has "authority"? Note, they were not defining it based on their OWN papal or Magisterial authority.
Then Trent may or may not have mentioned the concept, but certainly never defined what must be believed about it. St. Robert Bellarmine clearly limited it to catechumens, teaching resolutely the VISIBILITY of the Church. Others had different ideas. There were about as many applications of "BoD" (a phrase that exists NOWHERE in Trent) as there were theologians. Some that it applies to only catechumens, others to anyone with believe in the Holy Trinity and Incarnation, some to the American Indians who never heard of the Gospel, and Hindus in Tibet. Trent did not teach that it must be believed in, only that one had to AT MINIMUM hold that the votum is required for justification ... to avoid the heresy that the Sacraments are not necessary for salvation. In other words, Trent did not close the debate but left it open ... just as later the Church left Molinism open. Allowing Molinists to hold and teach it is not the same as teaching Molinism or endorsing it. If one applies the Cekadist principles, and those of Xaiver, the Church teaches Molinism and Catholics must believe it. But they must also believe in the Thomist position ... at the same time, since the Church allowed that to be taught too. Absurd. Simply because the Church did not resolve a debate, that doesn't mean that one side or another isn't simply WRONG. [Molinism and BoD are in fact tied together, BTW].
So we see that BoD is nothing more than a debated theological speculation. ALL THE ROADS OF BOD trace squarely and clearly back to one idle speculation by St. Augustine that he later rejected. THIS is the matter for revealed truth? That makes a mockery of the Deposit of Revelation.
Meanwhile, we see the pernicious fruits of BoD everywhere. BoD applied to anyone beyond a Catechumen leads to "αnσnymσus Catholicism," the concept that the Church includes not only actual Catholics (and catechumens) but even heretics, schismatics, and infidels (despite the fact that the one dogmatic EENS definition clearly said they were outside the Church). So you have this Frankenchurch ecclesiology, the one that was the foundation of all of Vatican II, and we then see the fruits of Vatican II. BoD extended to anyone other than, perhaps, a catechumen leads demonstrably to religious indifferentism.
So the BoD zealots are aiding and abetting the universal destruction of the Catholic faith into religious indifferentism. Rather than fight the TRUE errors, those which result from extended BoD, they spend all their time attacking those who believe that God will in fact provide the Sacrament of Baptism to all of His elect. So few people believe in EENS anymore, and their venom is reserved for those few people who still believe these things. BoD zealots are an enemy of EENS dogma, whether or not they pay lip service to it.