Not so. Birth announcements are put in like death announcements - by the family. Nobody's saying he didn't live in Hawaii, or even that he mightn't have been a natural born citizen if his mother had taken him down to get him registered. But we don't think she did. And his father was foreign, and his mother was underage, so the automaticity of his citizenship is in question.
You’re Indian, here’s a good example. My lab partner at school is Indian. She wants to take a graduate research assistant job at the school. In order to get it she is going to have to fly all the way back to India to get her visa status changed. Every i must be dotted and every t must be crossed, and there is still an element of uncertainty involved.
Now why should a lowly graduate student have to jump through all of those hoops, yet the candidate for the most powerful job in the world does not? It is nonsensical and unfair that he should not have to prove definitively his citizenship status.