Nah, actually I agree with you. What counts as believe and what as fact is rather abitrary. Is 2+2=4 a fact? Is global warming a fact? What about man-made global warming? Ask 100 people whether something is a fact or a believe.

To top that up, it's fact that there have been "proves" that were wrong (or maybe that's just my believe? :^]) even for a long time.

Hence, I think we can say that there are 4 options for a theorem:

1) Some mathematician believes the theorem is correct (but can't prove it)

2) Some mathematician believes the theorem is incorrect (but can't prove it)

3) Some mathematician believes the proof of a theorem is correct

4) Some mathematician believes the proof of a theorem is incorrect

Proving that a proof is correct is kind of meaningless. At that point it's all believe anyways.