I agree.
It is the way you have been applying the surrounding framework of what it means for Congress to "naturalize" is where there is solid ground for disagreement as to what it means for Congress to naturalize (an active verb there) a citizen, by statute.
Congress does not "naturalize" anyone who is otherwise born a citizen, even if clearly enough citizen under laws written of just who (just how and why) a person either is, or is not considered a citizen at time of birth.
There is no workable distinction between "born a citizen", and being a natural born citizen.
That begs the question. Who is otherwise a citizen? Where do you look to figure out who is otherwise a citizen, if we don't look to Congress?
-- There is no workable distinction between "born a citizen", and being a natural born citizen. --
Tell that to SCOTUS. They use a different framework, the legal one.
Congress is empowered by the Constitution to 'establish an uniform Rule of Naturalization,' Art. I, S: 8. Anyone acquiring citizenship solely under the exercise of this power is, constitutionally speaking, a naturalized citizen.