Actually it's not true or false. It's never been determined if someone born of a foreign national parent, but in the US, is "natural born". The only time the question arises is in eligibility for the Office of President. The only President known to have fit that description, other than BHO, was Chester Arthur, and his situation was not completely known until well after he left office. His father was not a citizen at the time of his birth, although, unlike BHO's father, he became one later.
This seems suspicious to me, so I looked briefly.
James Buchanan, Sr. was born in County Donegal, UK and was a subject of His Majesty George III (by British law) at the time of James Buchanan's birth in 1791. By this specious argument, President Buchanan could not have been "natural born", and he was not a citizen in 1788 (not yet being born). There may be others, but that one stands out.