If a baby is born outside of the United States but to an American, he is still eligible to be President. When a baby is born to an American, he is an American. This is why McCain is eligible, not only because he was born upon a military base.
Arnold Schwarzenegger, however, was not born to an American. This makes him ineligible.
Barack Obama was born to an American. He is eligible.
Do you state the constitutional requirement?
But, if there is just one US citizen parent for the baby, then the rules that I quoted above for those born outside the United States apply and though the baby may become a "naturalized" citizen, they are not "natural (or native) born".
The only time this makes a difference is in running for President.
But those are the rules Obama and his mom had to abide by.
Actually- you have missed one of the points. The law at the time had specific qualifications for the one “US Citizen” parent involved. Obama’s mother did not meet the requirements for her child to be an automatic citizen (assuming he was NOT born in the US or a territory).