And the affidavit, with all its errors, does?
I will assume that you are not being disingenuous and are not aware that the birth certificate on file could simply be a registration of Obamas birth.
The state officials refer to it as Obama's original birth certificate and not a certificate of live birth.
But I assume that you're referring to the law allowing people to get a birth certificate at a later date. Assuming, for the sake of arguement, that means what you all think it means then now what? If you honestly do not believe Obama was born in Hawaii then you're back to the problem that there is not a single bit of solid evidence that Obama was born outside the U.S. No documents. No affidavits, other than those full of elementary errors. No nothing. So even if Obama presented his birth certificate tomorrow, you're still stuck with proving he isn't eligible to be president. You're not having a lot of luck in that area.
But there are recorded oral statements to that effect from his Kenyan relatives in position to know, if he had been born in Kenya. Also the statement,also recorded, of the Kenyan Ambassador to the US. That was later disavowed, claiming he was "misquoted", but like I said, it was recorded oral statement, with no "quoting" required. But in disavowing it, he also verified that he was the one who made it, not some actor pretending to be him.
But one does not need "solid evidence" to request more evidence, only a "probable cause to believe"