What I mean by that title is that the criteria for a statement to fall under Papal Infallibility (PI) do not include an opportunity for the faithful to evaluate the statement, decide if it is true or false, material dogma or heresy, and then, only if it is decided to be true material dogma would it be accepted.
Material dogma is all the truths on faith and morals taught by Tradition and Scripture. Formal dogma is when the Magisterium in fallibly confirms material dogma. Truths that are implicit in Tradition or Scripture can also become formal dogma.
So if a statement meets all 5 criteria:
1. the Pope
2. speaking ex cathedra (narrow sense), speaking as supreme teacher of the Church
3. defines a doctrine (definitively teaches)
4. on faith or morals
5. binding on the whole Church
then the statement is a formal dogma of the papal magisterium and requires the full assent of faith; the refusal to assent is heresy, and the penalty is automatic excommunication.
The first criterion is that the teaching come from the Roman Pontiff, not merely from a dicastery of the Holy See approved by the Pope. He doesn’t have to write the document, but it has to be issued by him. If the Pope were not the valid Pope, then it would not fall under PI.
If Pope Francis uses PI in his next encyclical, claimed by an Italian Bishop to be on Human Fraternity, then his critics will not accept the teaching, as they are filled with pride and already have rejected the Magisterium as Teacher. So they will try to claim that some of the criteria are not met. But as experts weigh in and each criterion is confirmed (not that this is necessarily to PI), they will be left with nothing by the claim that Francis is not a valid Pope. And denying his validity makes them sedevacantists and excommunicates them.
The Church will become smaller and holier over the next several years. Hold fast to each Roman Pontiff and to the body of Bishops; believe whatever the Magisterium teaches, even if it is difficult or contrary to your own understanding. That is Faith. Do not follow the arrogant into Hell.