His argument against computer checked proofs is wrong, because doing a computer checked proof for your claim is NOT NEARLY as common as wearing your seat belt is. If it were, then all the big proofs would come with a computer checked proof, just as wearing a seat belt is normal when seeing the police nearby.
I don't think it's an argument against computer checked proofs. He even seems to acknowledge that automatic verification is a good idea. Unfortunately the world we live in is filled with proofs that cannot be checked by a computer.