Natural born refers to someone who can be nothing else because both parents are citizens of the United States and the birth occurred within the jurisdiction of the United States. A "law" or "statute" is not required to determine your citizenship stature, these are man-made definers as opposed to your natural condition defined by the nature of your birth circumstances. Thus "natural born".
The naturalization act of 1790 says that a person born to a citizen parent beyond the shores of America shall be as natural born, meaning the same. It is what set the precedence that being born inside the boundaries of the US is NOT a requirement of NBC.
You are correct.