I never accepted the proof of the original, because in my view a proof needs to be convincing as well as correct. Not every mathematician has this view, but language-wise I'd prefer to call the original proof a "verification of correctness" rather than a proof. The new proof is similar - more of a formal correctness verification.

What is the point of proof if not to actually convince the reader that the statement is correct? After all, most modern pure math is not terribly relevant to solve practical problems anyway, so if it's not convincing, then what?