A birth certificate is considered legal proof of place of birth.
You don't trust him. Fine. You shouldn't. But that's why there's the added provision of the state confirming the birth certificate.
I want them to confirm the information on the BC, not just the fact of it's existence. It's completely possible to have a BC on file with the state of Hawaii, and not be a natural born citizen, so merely confirming that the state has one on file is not sufficient. If the state sent a copy of the BC to interested/concerned parties, then that would at least be sufficient to prove where he was born, who his father was (and was he a citizen or not). Those are enough to determine natural born citizenship, under any of the alternate definitions.