Must Cameron have 100% certainty to be a Catholic?

I just listened to this "conversation" on YouTube between James White and Cameron Bertuzzi and wanted to comment on part of it. I'll spare you the whole background that led up to this conversation, but it's important to touch on some of it.

Cameron is thinking about joining the Catholic church, and lately he's taking a look at whether he should adopt the Catholic view of Papal succession and all that it entails. His approach is Bayesian, which James thinks is a mistake.

James' argument is that since the Catholic Church has defined the Pope and the Church as infallible, there can't be a Bayesian analysis of it. If you accept Papal infallibility, then this must push you to 100% certainty of everything the Catholic Church teaches dogmatically.

Cameron said he thinks that's false, and I agree with him. Unfortuantley, James wasn't interested in Cameron's reasons, so we never got to hear them. Instead, we just got to listen to James monopolize the conversation and lecture Cameron.

Let me speak in generalities here because although I don't accept the infallibility of the Teaching Magisterium of the Catholic Church or the infallibility of the Pope or anything like that, I do accept the infallibility of the Bible. So let me just talk about infallible sources in general. Does it follow that if you accept that there's some infallible source of authority that you are logically obliged to have 100% certainty about everything that source says? My answer is definitely not.

Now, James is right that if some source of authority is infallible, then by the very meaning of the word, it follows that they are 100% reliable. The reason you can accept that a source is 100% reliable without having 100% certainty about evrything they say is because you yourself are not 100% reliable. Your belief that the Pope or the Bible is infalliable is not itself an infallible belief.

It's possible to believe the Bible or the Pope is infallible, but to believe it with less than 100% certainty. I may believe the Bible infallible but acknowledge that I could be wrong about that. Maybe I'm only 90% sure that the Bible is infallible. The mistake James made was in conflating these things. He is confusing the Pope's infallibility with Cameron's infalliblity and acting as if one entails the other. I see a lot of presuppositionalists make this kind of mistake.

So no, if Cameron uses Bayesian reasoning to conclude with 80% confidence that the Pope is the infallible head of the Catholic church, this doesn't obligate Cameron to be 100% certain about everything the Church dogmatically proclaims. At most it only obligates him to be 80% certain of everything the Catholic church dogmatically proclaims.

I don't know if that was going to be Cameron's response or not because James wouldn't let him explain himself, but that's what I would've said. Although I'm on James' side theologically, I think Cameron was right and James was wrong on this issue.