Natural Born Leaders

The Constitution says "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". I've always understood "natural born" to mean a citizen by virtue of being born within the United States (being born within the US automatically bestows citizenship). The next election is gearing up to be a unique one, because both John McCain and Barack Obama were born on American military bases outside the United States (McCain was born in Panama and Obama in Hawaii before it was a State). Such bases are considered American soil, so they are both eligible for the Presidency by this definition. The New York Times recently tried to challenge whether McCain is really eligible for the Presidency, but their arguments are fallacious and would apply equally to Obama.

However, it looks like I was misinformed; the Volokh Conspiracy challenges my understanding of "natural-born", arguing that "If the drafters of the Constitution had wanted to require that presidents be born in the United States, they could have done so. Instead, they invoked the then-standard idea of natural citizenship as reflecting natural allegiance to the king or the state". As always, the comments are worth reading as well.

Update: I'm informed in the comments that Obama was actually born after Hawaii became a state (which happened in 1959). So I'm doubly misinformed. In the age of the Internet, there's really no excuse for that. My apologies.