Wife and I are both US citizens, born in Arkansas and Maryland to US citizens, we have two sons born overseas at military bases (Philippines and Iceland). Would you say they are natural born citizens?
I didn't think that was fair.
The simple fact is I don't know, and neither do you, nor does anyone else. Under law Natural Born Citizen" has never been defined save that one time in the 1795 law, which was repealed in 1796.
There was also a "sense of the senate" declaring Panamanian born John McCain an NBC. Not a law, but giving further privilege to Juan of their own. And you and I both know that should he have been elected (God forbid!) the democrats would have used it to undermine his authority!
Until and unless the supreme court or congress sees fit to define it, it will be the subject of endless debate.
Since I believe that that one office, that of the President of these United States, must be free of any hint of divided loyalties, I would say no, a child born in the Philippines (where we have fought shootin' wars) or Iceland (which was a key cold war base) lest our enemies, foreign and domestic, stir up trouble in those countries and put that president in a politically untenable position, no matter anything he does or doesn't do.
I still don't think it's fair, but I think it's sufficiently important that the commander in chief have nothing that can be twisted to damage his authority in times of conflict, that the NBC standard be as restrictive as possible.
YMMV