"Under the jurisdiction of the United States" I believe would be the qualifying principle here, and yes, SCOTUS would have to clarify it. I think they'd have to look at the repealed 1790 law that stated children born abroad of U.S. citizen parents would be considered as "natural born" -- but didn't that law NOT include specifically mention of people abroad in the service of the United States? I think the intent would be that anyone under the "sovereign reach" of the United States would be considered as "under its jurisdiction" as much as the ones born on U.S. soil.
"Born on U.S. soil," however, is a distinction clear enough for the layman to understand.
Wiki talk page argument on what "natural born citizen" means: http://en.wikipedia.org/wiki/Talk%3ANatural-born_citizen
. There is no mention of NOT granting "NATURAL BORN STATUS" in the 1795 Naturalization Act to a child born outside the U.S.. Checked several references ( Wikipedia, National Archives, ect.) and they all said basically the same thing.