The Panama Canal Zone in 1936 was as much a US Territory as Hawaii and Alaska. How many US Presidents were born in territories?
Andrew Jackson is the only one I can think of, There was some bustle about AuH2O, but it didn't get much traction. Of course, the first presidents weren't born in the US because there was no US to be born in, but the Constitution explicitly exempts them.
It is possible that a court could exclude someone born to two US citizens on US territory from the status "natural-born citizen," but I find it incredibly unlikely.