Which is exactly right.
IMHO, the biggest confusion comes because people nowadays automatically think of the federal government as 'sovereign' in it's relationship with the States, and thus can 'dictate' Law just like the King.
In fact, the opposite was true.
The common law has affixed such distinct and appropriate ideas to the terms denization, and naturalization, that they can not be confounded together, or mistaken for each other in any legal transaction whatever. They are so absolutely distinct in their natures, that in England the rights they convey, can not both be given by the same power; the king can make denizens, by his grant, or letters patent, but nothing but an act of parliament can make a naturalized subject.
This was the legal state of this subject in Virginia, when the federal constitution was adopted; it declares that congress shall have power to establish an uniform rule of naturalization; throughout the United States; but it also further declares, that the powers not delegated by the constitution to the U. States, nor prohibited by it to the states, are reserved to the states, respectively or to the people. The power of naturalization, and not that of denization, being delegated to congress, and the power of denization not being prohibited to the states by the constitution, that power ought not to be considered as given to congress, but, on the contrary, as being reserved to the states.
St. George Tucker
Before a foreign national could fall under the naturalization rule, he must first be made a denizen , or legal alien, by the Sovereign authority of the State of his residence.
Not to mention that this residency, denizenship and naturalization process does nothing other than to create a positive law citizen.
As you've said, only Natural Law can define a natural born citizen.
Your St. George Tucker reference started off with this:
“Prior to the adoption of the constitution, the people inhabiting the different states might be divided into two classes: natural born citizens, or those born within the state, and aliens, or such as were born out of it. The first, by their birth-right, became entitled to all the privileges of citizens; the second, were entitled to none, but such as were held out and given by the laws of the respective states prior to their emigration.
Then it goes all gobbledygook and very difficult to understand. But I dont think it is important to understand because it talks about various state rules, etc.
The issue at hand is the United States Constitution and its declaration that only Natural Born Citizens are eligible for the office of president. Not interested in getting into each individual states laws and customs, the framers wanted someone who was physically born on U.S. soil, at least 35 years old and a resident for the previous 14 years certainly enough time to be devoted to the country. That length of time would certainly satisfy Jays concern.
When coupled with all the other evidence available I am 100% convinced that this republic does not require citizen parents to be it’s president. See quoted reference to MamaTexas. http://www.uniset.ca/naty/maternity/9YJLH73.htm.