[El Gato]

For that matter, not one branch of the federal government has any authority over the subject of citizenship....only the provision that they make immigration 'regular'.

Not what the Constitution says. It says:

The Congress shall have Power...To establish an uniform Rule of Naturalization.
Article I Section 8

Thus someone who is a citizen only by virtue of some provision of the US Code (ie. a law passed by Congress) must be a naturalized citizen, even if naturalized at birth. They cannot be a "natural born" citizen.

[MamaTexan]

To establish an uniform Rule of Naturalization.

Thank you for the correction.

However, having the legitimate authority to make the rule for naturalization uniform does not bestow the authority to control or define every aspect of citizenship.

It only means Congress gets to make the rule so the criteria for being a naturalized citizen will be the same for every State.