Those parents, or generally the father, are serving the country, even though outside of it. Vattel's law of Nations apparently has an "exception" to the normal rules for persons serving the country outside it's borders.
I left out the quote and section, it's 5 sections down from the "natural born" definition.
§ 217. Children born in the armies of the state.
For the same reasons also, children born out of the country, in the armies of the state, or in the house of its minister at a foreign court, are reputed born in the country; for a citizen who is absent with his family, on the service of the state, but still dependent on it, and subject to its jurisdiction, cannot be considered as having quitted its territory.
I seem to remember something about that in the "Wong Kim Ark" case, where it was stipulated that Wong's parents were not in the service of the Emperor of China. ... Yep, part of the stipulated facts.
That during all the time of their said residence in the United States as domiciled residents therein, the said mother and father of said Wong Kim Ark were engaged in the prosecution of business, and were never engaged in any diplomatic or official capacity under the Emperor of China.
That pretty much implies that if they had been, then Wong would have been a subject of that Emperor, not a US citizen imder the 14th amendment, as the Supreme Court found him to be, due to his birth in the US, "subject to it's jurisdiction".
More importantly, so does federal law. But are you saying that if federal law said such persons were not natural-born citizens you would insist that they were? Because Vattel said so?