Indeed, the United States is one of the few nations where your citizenship is determined by your birthplace, and not your parents nationality (if your German parents birthed you while traveling in the U.S, you would be both a German and U.S citizen). Interesting, no?
However, I would think that a U.S military base would be considered U.S soil much like an embassy is. However, America is inclusive, if you were born to an American mother, no matter where you are, you are considered a U.S citizen... If you were born to an American father only, however... tough luck (sorta).
The wiki page on the subject is actually rather interesting...
http://en.wikipedia.org/wiki/Birthri...tes_of_America