So, by your reasoning anyone can serve as POTUS, because, according to you “natural born citizen” is nowhere defined in law.
No, that’s not my reasoning. It’s clear from various court decisions that a child born to two citizen parents under US jurisdiction is a natural born citizen, but it’s not clear that a child born under other circumstances is a natural born citizen. That does not mean that such a child is not, but it creates doubt. Such doubt apparently can be resolved, again according to various court decisions. However, there has been no occasion to resolve such doubts up to now.