It's supposed to be, but there are different concepts of natural law. There's not one single concept of what natural law is supposed to be.
The kind of natural law that gave us the term natural born citizen derived from the "natural law" concept that if you were born in a particular country, God intended that country to be your country. It didn't matter whether your parents were citizens or not.
And a term that started out referring solely to perceived natural law can be modified over time, through the consideration of new situations not originally considered.
My point was that a resort to natural law is generally a weak argument. There is no authority to resort to, no proof to present, no objective standard of weighing one person’s conception of natural law against another’s. It’s like a postulate in mathematics — it should be used as a basis only for the most fundamental principles that cannot rest on any other foundation. Much is derived from them, but they cannot be derived; but without them, everything falls apart.
“That all men are created equal; that they are endowed by their creator with certain inalienable rights; that among these rights are life, liberty and ...” property; “That to preserve these rights governments are instituted among men, deriving their just powers from the consent of the governed.” That kind of thing.
These principles are fundamental. They are eternal. They are also not very specific as to ways and means. The law of citizenship, on the other hand, is very much contingent, and very, very specific. For starters, for most of human history, even “citizen” was a novel term; people were natural born or foreign subjects. There is nothing fundamental to the notion of ordered liberty about who is or is not considered a citizen.
For a question like the natural born citizen clause of Article II, an appeal to natural law is fruitless. It can much too easily go either way. The first resort should be to the black letter law; then to the intent of the Framers to the extent it can be determined. The problem with that latter step is that the Framers often did not share a consensus view. The vague language in the Constitution is intentionally so; the Framers could not agree amongst themselves, and left the details to the small-r republican and, to varying degrees, small-d democratic institutions they were building.