Yeah, I've heard about this "notorious difficulty" in verifying proof checkers before, and I don't understand what it could mean. Humans are way more unverifiable.

I think the idea is that for a point this controversial he is well aware that mathematicians may actually object to his trustworthiness (they've objected to less questionable things in the past), and want to verify the proof for themselves. I think he may well be right in this. However, I don't see why he can't give a full explanation (his current paper isn't) for humans as well, since this would probably be finished sooner and would probably save a lot of his own time if there is a mistake.