At present those born in all of those territories except American Samoa gain U.S. citizenship at birth and thus would satisfy the native-born citizen requirement
Why there's an exception for American Samoa?
Yes, but when he was elected, he was a resident of a state. The same applies to Barry Goldwater, who was born in then-Arizona territory, but when he ran for President, he was a resident of the state of Arizona.
Hm, I never really thought of that thing, since I always thought of territories simply as part of the United States, not quite realizing meaning of "unincorporated".
Anyway, thanks for your great response, as always