LoT,
As you have pointed out, this part of Fr Boulet’s argument is disingenuous. In effect, he is applying the straw-man fallacy.
On your other point:
Whether a true pope can fall into error in his teaching on matters of faith and morals.
In the Gospel according to Saint Luke, we read in chapter 22:
(31) Ait autem Dominus Simon Simon ecce Satanas expetivit vos ut cribraret sicut triticuм:
(32) ego autem rogavi pro te ut non deficiat fides tua et tu aliquando conversus confirma fratres tuos
[Vulgate]
(31) And the Lord said: Simon, Simon, behold Satan hath desired to have you, that he may sift you as wheat:
(32) But I have prayed for thee, that thy faith fail not: and thou, being once converted, confirm thy brethren.
[Douay-Rheims]
It is to be noticed that in verse 31, the personal pronoun (vos) is plural, referring to all of the Apostles; whereas in verse 32 the personal pronoun (te) is singular, referring to Simon Peter as the head of the Apostles. Thus, in these words Our Lord, just before His Passion, warned the Apostles that they would all be attacked by Satan, but also advised that, in advance of the attack, He had especially prayed for the endurance of Peter’s faith, even then knowing that Peter’s courage would temporarily fail him. But having recovered, it would be Peter’s duty to confirm the others in the faith. With the birth of the Church at Pentecost, we see Peter boldly fulfilling this mandate.
From this, I deduce that the divine protection of the faith in Peter and in his successors is guaranteed by Christ. If it were not so, then the Church would be without an infallible final court of appeal, and each of us would be left to his own devices to divide truth from error.
Therefore, I am drawn to the conclusion that, being under a special form of divine protection for the good of the faithful, a true pope cannot fall into error in his teaching on matters of faith and morals -- as in fact the Church teaches.
On the other hand, when a purported pope, either by his words or by his deeds, gives public expression to errors of this class, it must follow that he lacks the divine protection proper to a true pope, and that, lacking this protection, he was never a true pope from the outset. If it were not so, then, in principle, it would be left to the faithful, each to become a mini-pope sifting out the errors from the public expressions of the maxi-pope -- which is absurd, and a formula for every flavour of Protestantism, for quis custodiet ipsos custodies?
To put this another way, it is inimical to my way of thinking that a genuine pope should ever fall into error in his teaching on matters of faith and morals. -- A point of view, which I think you share.