If slaves and the children born of slaves were not Natural Born citizens, then the term Natural Born Citizen has nothing whatsoever to do with Natural Law.
That is assuming that black slaves were considered by slave owners to be fully human.
In the same way that the unborn are NOW not considered to be human, the slaves were largely considered to be less than human.
More like, you have an erroneous understanding of the concept of Natural Law as understood by the founders.
How can people who are not members of a nation become members of a nation without the acquiescence of the existing members of a nation?
They weren't born into it, so the only way they can acquire membership is by adoption, and that was with-held until 1868.
I do not even understand where you are coming from with your argument.
Citizenship is a mixture of what the people are doing (which they will do no matter what country claims to be ruling over the territory they live in), and what the government does.
The conventional legal mumbo-jumbo, which is pretty old and has a reasonably consistent history, is that when a new country takes over a territory, it can "naturalize" wither into citizens or nationals, the people who live there.
The founders were naturalized into US citizenship by the act of rebellion, successfully carried out against the prior government who claimed dominion over the territory.
Citizens of the US were defined in the constitution as citizens of the states, and the slaves were not considered citizens. That too is a legal construct.
When the 14th amendment passed, slaves who were living were naturalized, just as the citizens in the colonies who were not British loyalists were naturalized by the revolution.
As far as I can tell, this "legal usage" convention is not contentious at all. Sometimes there is contention over an individual, but the issue there is "citizen or not citizen," so the difference between naturalized and natural born is immaterial. The debate over the meaning of NBC is a tiny twig off the branch of citizenship law.
Back to your point, the ex-slaves where were naturalized by the ratification of the 14th amendment would not be considered natural born; any more than the founders considered those born in the colonies under British rule to be "natural born US citizens" by dint of a later revolution. That "usage" is why the grandfather clause exists in the constitution.
I do agree that this has nothing to do with natural law. Nothing in the law is natural. Everything in the law is dictated by some decider, a judge, a legislator, a bureaucrat.