Nice find.
I am certain that the founders wanted to ensure that the president of the United States did not have mixed loyalties and hence the requirement of being a Natural Born Citizen would imply that the person must be born under the sovereign jurisdiction of the United States of America. I am not certain that simply because Obama's mother was a United States Citizen, that makes any child she bears while domiciled outside the United States a "Natural Born Citizen".
The fact that he has not provided a copy of his actual birth certificate suggests to me that he was not born in the United States. Even if that were irrelevant to his constitutional qualifications, it would certainly be relevant to the electorate in deciding whether or not to elect him.
Obama needs to come clean on this one.