Lets go through a simple thought exercise. Let set up two people Mr. A and Mr. B Both claim to be US citizens. One has his citizenship confirmed by US Law (Mr A) and one CLAIMS to be a US Citizen but there is no US Law confirming his citizenship (Mr B)
Who is in fact, a citizen? Not Mr B because the laws don’t support his case NO MATTER WHAT HE CLAIMS. In other words, the law/act/statute is there to direct the will of Congress on the government and control the behavior of government with regards to how it treats the People.
Since “natural law” is NOT BINDING on the US government, Mr B can shout and shake his fist, but he is NOT a citizen of the US until there is an established rule making him a citizen of the US. Be it by birth or by naturalization.
Let me ask you this, a citizen who was not a citizen at birth is called a naturalized citizen. What do you call a citizen who was born a citizen?
That depends: there are naturalization laws which set forth birth conditions as grounds for their citizenship, they are therefore naturalized citizens.
Again, just because they're naturalized at birth doesn't mean that they are natural born; and there is a huge flaw in your "confirmed by law" argument — this is that if it is a law passed by normal legislative action then it can be repealed and modified by normal legislative action, and if that is the case then it cannot be used to define natural born citizen
because if that were the case then the legislature would be able to alter the constitution by its normal operations and this, in turn, would mean that the constraints proscribed by the constitution would be useless because the normal operation of the legislature could alter it at its whim.