Lots of bizarre things about "de presbytero non baptizato". Apart from the fact that how can you have an unbaptized priest, Innocent "asserts without hesitation that ... this priest [went to heaven]" ... continuing to call him a priest, and somehow declaring that this man went to Heaven. I guess we should immediately canonize this priest, since we have Innocent III's authority for it. Then he "asserts without hesitation" [that this priest is in Heaven] "based on the authority of Augustine and Ambrose". He does not teach it, but rather "asserts" (as if he were in a debate and opining in favor of it) nor is this letter addressed to the universal Church, and does not teach it by the authority of Sts Peter and Paul, i.e. his papal teaching authority, but on the authority of St. Augustine and St. Ambrose. So now Augustine and Ambrose have the authority to define a dogma? Of course, he's mistaken in appealing to that authority, since St. Augustine never taught it with authority, but rather clearly indicated that it was his own speculation, and retracted it later in life, and St. Ambrose didn't teach it at all (that's a misreading of his oration on Valentinian). In a similar letter, Innocent proclaimed that the consecration at Mass would be valid if a priest merely thought the words but did not say them out loud.
Not only does this "de presbyter non baptizato" not meet the notes of infallibility, where the Pope is teaching something with HIS Apostolic authority, the authority of St. Peter, and teaching something to the Universal Church, that must be believed. He's leaning on the authority of St. Augustine and St. Ambrose, who have no authority to define doctrine for the Church, and is clearly opining ("assert" to does not mean to teach authoritatively, but merely to argue or to opine).