IMHO, a birth certificate is required as documentation in applying for a US passport.
He may have many other fraud violations relating to school, credit cards, banking and mortgages if his citizenship is not proven.
Just saying
It isn't.
Further, I'm not really sure that a birth certificate would be particularly informative in any case. When people are adopted, it is common for new certificates to be issued and for the original ones to be sealed and in some cases destroyed. If someone who was adopted anonymously were to later run for President, I'm not sure that they or anyone else would have standing to unilaterally demand that their birth certificate be unsealed to prove that they were actually born in the USA.