Edit: I should add that this is already a problem for, ironically, computer-assisted theorem proving. If a computer produces a 10,000,000 page "proof" of a mathematical theorem (i.e., something far longer than any human could check by hand), you're putting a huge amount of trust in the correctness of the theorem-proving-software itself.

No, you just need to trust a proof-checking program, which can be quite small and simple, in contrast with the theorem proving program, which can be arbitrarily complex and obscure.