I amend my previous post. Cboldt is correct. The key factor is the parents being subject to the jurisdiction of the United States. This was precisely the situation with John McCain's birth.
Yep. I think what the founders were aiming to do was limit the presidency to those people who were born to and would be raised by citizens. And in the day, families were "ruled" by the father, making citizenship and allegiance of the father most important.
McCain was born outside the country, and therefore needed some different method for being ‘natural born’.