"All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside."
They are not born/naturalized in the United States, but one of its territories. "Subject to the jurisdiction" is satisfied, but the other part is not.
(We can grant citizenship to territories by statute, like Puerto Rico, but the Constitution does not mandate it. American Samoa, thus far, doesn't seem to want it.)
"All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside."
They are not born/naturalized in the United States, but one of its territories. "Subject to the jurisdiction" is satisfied, but the other part is not.
(We can grant citizenship to territories by statute, like Puerto Rico, but the Constitution does not mandate it. American Samoa, thus far, doesn't seem to want it.)
The history of this is all a bit gross. https://en.wikipedia.org/wiki/Insular_Cases