You know, when you actually look at the Constitution...
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
That looked a bit fuzzy to me. When I looked up the background, turns out there's a lot of background to look at.