Your statement is true...

....in it's pure, unadulterated form.   However, you sometimes floor me with satements containing no factual substance.   The old Panama Canal Zone was from 1903 to 1979 strictly under US control, in fact, Panamanian citizens could only enter with restrictions.  A person born in the Zone within that period of time, would NOT have under any circumstances be subject to Panamanian, or foreign jurisdiction.  In fact, anyone born in US controlled areas or military bases, is a US citizen, not a citizen of the surrounding country.

Take these two instances as examples:  If two service persons were to have a child while in the US military and stationed at Guantanamo base, that child would be a US citizen. Period.   The child would not be recognized by Cuban authorities as a Cuban nor would the child be under Cuban jurisdiction, because the Guantanamo Base, although technically in the island  of Cuba, is not Cuban, it's US territory.  If someday the base is returned to Cuba, (which is a matter for another discussion in its own right) then persons born at that time would indeed be Cuban citizens.

Another instance is Puerto Rico.  As it stands right now, all Puerto Ricans, whether born in the balmy Caribbean Island and nurtured with 'arroz con gandules', or in one of America's large cities, are all US citizens and could run for president if so inclined.....because the circumstances above describe instances of people born in US territory where they can be nothing else besides US citizens and under no other jurisdiction than the US.

Eventually, and I don't remember the year becasue I have not made it a matter of serious observance, the canal zone was returned to Panama, and I would dare say that anyone born now in what was once American territory, is solely a Panamanian citizen.

There are a few other individuals who were born in various US territories outside the mainland and have run for president, besides McCain; Barry Goldwater being one.  Ther are others whose names I don't remember either.

NOTE:  I don't personally want McCooties to win the presidency any more than I want to see the other two disasters in the making, but I should hope that the American people would be sharp enough to find the many genuine reasons to keep this person out of the White House beside some ridiculous misinterpretation of birth status!