Nobody knows for sure. McCain was born in what is now Panama. He might’ve been born on “US Territory” in the sense that we had control over the Canal Zone at the time, or it might’ve been just across the border in a hospital in Panama, nobody seems to know for sure. But he’s the first real nominee not to have been born on “U.S. territory” (Goldwater was born in AZ before it was a state).
Having studied all of this for a number of years, I think an honest reading of the provision would say that for that one particular office, the Presidency, the Founders intended to exclude anyone with even the smallest shred of potential for divided loyalties, and as such only someone born “on the land” to two citizen parents would qualify, with exception for military and diplomats overseas. Anyone else has at least some sort of claim to citizenship somewhere else, and as such could have divided loyalties.
The constitution is harsh this way, it looks at us as purple newborns, and we're stuck with that label forever. There is no way to know where that person's loyalties end up. Follow mom? Follow dad? Renounce and choose another country?
It's an imperfect system, but there is none devised, that is better.
“with exception for military and diplomats overseas”
Where do you find this? I’ve been told my many arguing that Cruz is not considered Natural Born that my children also do not qualify even though they were born while I was serving this country overseas in the US Army and I was born in the state of Oregon.