In this case the human written statement of the theorem is small. Can there be bugs? Absolutely! But it's essentially a few lines of code worth of thinking.

The lean proof checker then checks to make sure the proof actually proves the statement.

In this case an AI is generating the proof, but if it "compiles" it's correct. The only thing humans need to check is the statement to be proven.

(I don't know anything about this project but I've played around with lean and used other proof checkers more sesrisously).

This is also an issue with non-AI and non-Lean proofs. Andrew Wiles' initial Fermat's Last Theorem proof initially had an error in it. That was spotted by peer review, fixed, and an updated proof was submitted.