No one knows for 100% certainity.

Because Hawaii wasn't yet a state and the way things were set up it is near impossible to prove at this point that he was born in Hawaii. In turn the only way one could prove that he was born in Kenya would be if he or his parents stated so. 

Obama DOES have a birt certificate and that is not the problem. In those days Hawaii wasn't yet a state and you just applied for one at a later date. It is possible he was born elsewhere and then applied for a birth certificate. Knowing that Hawaii would become a state and knowing that being born in the United States has always had advantages over being born in a place like Kenya it is feasable to believe that parents might make this choice.

Does it matter? In this case I really don't think so. He pretty much has lived here his whole life and Kenya isn't a huge part of today's issues a president must deal with.

Imagine however someone not born here who perhaps lived most of his life somewhere else. If president such person might make decisions that would benefit that other country over our own. Take it further, Imagine that county was involved in a war and the president had land and family there. Also imagine a foreign country that had designs to place someone at the head of our government. Crazy as that sounds without the rule all they would need is the majority of the vote.

 So to play it safe it just stated that you have to be born here.

Or better yet, what if he was born there but his parents lied to him and told him he was born in Hawaii and he believed them (you pretty much gotta take their word for it hehe) would it be his parents that got in trouble?