Barry Goldwater was born in Arizona when it wasn't a state. He ran in 1964 and would have won if millions and millions of people had voted differently. Wouldn't it be the same thing?
Well Goldwater probably inherited birthright citizenship from his two American citizen parents, but even if he didn't the real difference there would be that anyone born in the Arizona territory was a U.S. citizen at birth according to federal law. This is true today of Puerto Rico, Guam, etc. American Samoa, however, is an
unincorporated territory, so being born there does not automatically confer citizenship.
