If you need to go through the naturalization process in order to become a citizen, you are not “natural born.” Otherwise, you are. It really is that simple, regardless of how some want to make it complicated.
I agree, if “Going through the naturalization process”...also includes birthright citizenship, as it should because this is also citizenship bestowed by state law, not as a consequence of natural law.
That's not accurate. Any person born to an American female on foreign soil is a "citizen" who did not have to go through the naturalization process because congress made their naturalization automatic. (Rogers vs Bellei comes to mind.)
The 14th amendment is exactly the same. It naturalizes large classes of people without resorting to any process beyond being born on US land.
But these sorts of automatic naturalizations are very different from "natural born citizens."
A "natural born citizen" does not require any sort of positive law to be a citizen. They are a citizen by the operation of natural law, i.e. "nature."