Certainly, within the structure of the judiciary and within the Bill of Rights, the framers adopted aspects of Natural Law. That doesn't mean they also intended to adopt all aspects of every competing theory of Natural Law. It is not a unified body of thought, and it's just not capable of answering most detailed questions. Once you get beyond "murder is wrong", "stealing is wrong", and "you can't be a judge in a case in which you have a vested interest", its usefulness is pretty limited.
Do you recognize that a child born within the borders of the US of US citizens is a Natural Born Citizen?
Maybe in common law, definitely in written law, but under which theory of natural law do you see it?
No, it isn’t in written law, because it is based on self-evidence.
That’s why so many people are whining. “Why isn’t this self-evident definition in written law?” The answer is as simple as it is telling. Natural Law, as in my post, cannot be trumped by man’s law, common law, or any other written law.