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?
In the case of each of the other unincorporated territories currently held by the United States, there has been an Act of Congress that has granted the inhabitants citizenship.
Hawaii in 1900
Puerto Rico in 1917 and 1941 (1917 law provided for opt-in citizenship for all Puerto Ricans who requested it, 1941 law gave birthright citizenship to all born later)
Alaska and Virgin Islands in 1927
Guam in 1950
Northern Marianas in 1986
The local chiefs in American Samoa don't want an Organic Act passed for the territory or automatic citizenship because they think doing so would erode their authority, so they don't press for either. This is a bit of a controversy as there are some Samoas who do wish to change that, but it's not a priority for Congress. Those born in American Samoa to those who are not US citizens do become US nationals upon birth.
as did Vice President Curtis who was born in Kansas Territory.
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.
True, but I was addressing the native-born requirement, not the residency requirement.
If there is a potential sticking point for them it would be the residency requirement, as a President is required to have "been fourteen Years a Resident within the United States" and the status of our current territories as unincorporated territories would when combined with Downes v. Bidwell be taken as they are not resident within the United States while they live there.
In the case of Luis Fortuño, he spent some years on the mainland while in college, but I don't know if he has spent other time here sufficient to add up to the requisite 14 years on the mainland to make the residency requirement moot.
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
It's hard to say if the Insular Cases would be on point. There are some who think they are anachronistic, and it wouldn't be inconsistent with them to hold that the residency requirement would be satisfied by living in Puerto Rico given that birthright citizenship holds there. What probably would be the determining factor is that living in Puerto Rico counts towards the residency requirement for becoming a naturalized U.S. citizen under current immigration law. (So does living in the Virgins, the Northern Marianas, and Guam, but not American Samoa.)
Still, there is nothing explicit in the law, so if someone from Puerto Rico, Guam, the Virgins, or the Northern Marianas did end up on a presidential ticket, it could well end up being brought up in a court case.