CathInfo.com

For, if you understand by the expression material heretic one who, while professing subjection to the Church's Magisterium in matters of faith, nevertheless still denies something defined by the Church because he did not know it was defined, or,

This is not applicable to protestants because they either know the magisterium exists or they reject its authority.

by the same token, holds an opinion opposed to Catholic doctrine because he falsely thinks that the Church teaches it, it would be quite absurd to place material heretics outside the body of the true Church;

A protestant can't believe that the Church teaches something if they are "invincibly ignorant" that the Church exists.

while material heretics are those who, being in invincible ignorance of the Church herself, in good faith choose some other guiding rule.

This contradicts the middle quote.  He says that Protestants can only be material heretics if they are ignorant of the Church.
FAIL.  Billot fails in trying to explain the unexplainable.  This logic is ridiculous.  Typical modernist mumbo-jumbo.

I heard asimilar story about Edwin Edwards. He was αssαssιnαtҽd. When he was shot he was brought to a Catholic hospital. The nun asked him if he wanted to see a priest. He said, "No sister, I am not a Catholic." The sister held his hand and led him in making an act of perfect contrition. I believe this sister helped him to make his peace with God and that he could well be in Purgatory if not in Heaven by now. If the religious sister more than 80 years ago who probably never heard the word VaticanII  during her lifetime thought that because he wasn't a Catholic he would go straight to Hell tehn why would she waste her time leading him in making an act of perfect contrition?

So poche does theology based upon the sentiments of a nun.

This error long predates Vatican II, and it was in fact the cause of Vatican II.

So, poche, how do you explain this particular story in light of the dogma that there's no salvation outside the Catholic Church?

But the nature of heresy consists in withdrawal from the rule of the ecclesiastical Magisterium and this does not take place in the case mentioned [of someone who is resolved to believe all that the Church teaches but makes a mistake as to what her teaching consists in], since this is a simple error of fact concerning what the rule dictates. And therefore there is no scope for heresy, even materially."

If this accurately reflects the position of Billot, then this is an epic fail.  One need not ACTIVELY WITHDRAW from the rule of faith, but the rule of faith can be passively missing or absent.  Without this infallible and divine rule, supernatural faith is simply not possible.  Cf. St. Thomas ... and even the Catholic Encyclopedia.  It matters not whether the rule of faith has been actively rejected or whether it's simply absent and was never there in the first place.  If you want to play semantics and limit the term "heresy" to those who have actively withdrawn from the rule, whatever, but the essential truth is that no one who lacks the rule of faith can have supernatural faith.
Formal heresy is not to be equated with active sin; what formal means in this context is that the formal motive of faith is missing.  Billot wrote based on the false assumption that Protestants can indeed have the formal motive of faith that suffices for supernatural faith ... and then plays word games to make this fit.

Hypothetically, it is possible for someone to believe every single truth taught by the Church, but not believe it for the right reasons or with the proper formal motive.  Such a one would be a formal heretic, but not a material heretic.

Conversely, it is possible for someone to not believe the vast majority (everything but the core articles) and still have supernatural faith.