You're most probably right. But the whole idea of the "natural born" clause is to minimize foreign influence on the President. Would a person born in Germany, and presumably raised at least some of the time in Germany, have an innate pro-German bias? I think so, and that would be dangerous.
I sure wish the Founders had been more specific as to what "natural born" really means. IMHO, it should mean born in the USA, to parents both of whom are American citizens.
“I sure wish the Founders had been more specific . . .”
I believe they relied on, and may have referenced a definition extant. As I recall, it depends on being born on territory of the United States, which can be offshore, and there are certain exceptions having to do with military stationed in non-US Territories. But it requires more than a U. S. citizen mother in the case of an offshore birth.
That makes you anti-military, since there are lots of military brats, some of whom might make great presidents (no, not Crash, but he's a military brat), who do not fulfill your definition of Natural Born.
It's really simple: if you are entitled to citizenship by reason of your birth, you are natural born, even if the birth took place on the other side of the moon. Don't get confused by 18th-century furriners from Switzerland.