People are really confused about natural-born USA citizenship, and who has it. In fairness, sometimes it does take a court to decide, but, in fact, there are some clear rules. Taitz is simply wrong in what she claims is required. She (mistakenly) claims that in order to be a natural-born citizen of the USA, both of your parents must be citizens of the USA, so it doesn't even matter if he was born in the USA because his father was not a US citizen (he was a British subject).
FALSE claim. It does matter.
Obama was born in a state in the United States. That's the fulfillment right there. Children born to foreigners on our soil are natural-born US citizens by birth unless the parents are foreign ambassadors or consuls (there are a few exceptions), and Obama's mother was a US citizen. It does not matter that his father was not, and wouldn't have mattered if his mother was not. [source]
Obama held dual citizenship by birth until he turned 21, this is according to The British Nationality Act of 1948 and the Kenyan Constitution (Kenya became independent from Britain in 1963). He was American/British until Kenya gained independence from Britain. Kenya does NOT permit dual citizenship for adults, and to become a citizen of Kenya one would have to have renounced US citizenship and pledged an oath of allegience to Kenya at the age of 21. This did not happen. [source: FactCheck]
The wiki link does have some interesting historical examples of Presidential candidates and their citizenship issues. There's Chester A. Arthur (as Colbert mentions), Barry Goldwater (who was born in Arizona before it became a state), and the one whose eligibility really IS iffy: John McCain.
Like most people, I thought that a military installation counted as American soil. Not so. He is a citizen because his parents were citizens, but since he was not born on American soil it is still in dispute as to whether he is a "natural-born" citizen or some other kind. Here's an excerpt, you will have to visit the page for more info.
The former unincorporated territory Panama Canal Zone and its military facilities were not regarded as United States territory.[39] In March 2008 McCain was held eligible for Presidency in an opinion paper by former Solicitor General Ted Olson and Harvard Law Professor Laurence H. Tribe. In April 2008 the U.S. Senate approved a non-binding resolution recognizing McCain's status as a natural born citizen. In September 2008 U.S. District Judge William Alsup stated obiter in his ruling that it is "highly probable" that McCain is a natural born citizen, although he acknowledged the possibility that the applicable laws had been enacted after the fact and applied only retroactively. These views have been criticized by Gabriel J. Chin, Professor of Law at the University of Arizona, who argues that McCain was at birth a citizen of Panama and was only retroactively declared a born citizen under 8 U.S.C. § 1403, because at the time of his birth and with regard to the Canal Zone the Supreme Court's Insular Cases overruled the Naturalization Act of 1795, which would otherwise have declared McCain a U.S. citizen immediately at birth. Although the US Foreign Affairs Manual states that children born in the Panama Canal Zone at one point only became U.S. nationals, it also states in general that "it has never been determined definitively by a court whether a person who acquired U.S. citizenship by birth abroad to U.S. citizens is a natural born citizen […]". In Rogers v. Bellei the Supreme Court only ruled that "children born abroad of Americans are not citizens within the citizenship clause of the 14th Amendment", and didn't elaborate on the natural born status.
Obama's citizenship is not in dispute. The government has decided to trust the certification and paperwork from the State of Hawaii vs. the (real or fabricated) third-party (rightwing media) hearsay about the statement of Obama's Kenyan grandmother. McCain's citizenship really might have needed to be decided by the Supreme Court to get a binding ruling. (not saying that wouldn't happen, just saying there's a real controversy)
The FactCheck article also says that a Hawaiian source said that the Certification of Live Birth is really all they issue. I'd like to see some documentation on that just to put this to rest.