I also haven't heard anyone assert he's not American, even though he was born in Panama.

The constitution says (Article 2, section 1): "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'd love to disqualify McCain on this basis - hell, on any basis. But sorry, he was born on a military base, which is US sovereign territory, and that's as good as being born on American soil.