You assert that Congress has the power to natualize and that that power is limited to naturalization only.
That is not what the Constitution says. Allow me to quote the section directly from Article I Section 8:
To establish a uniform rule of naturalization, and uniform laws on the subject of bankruptcies throughout the United States;
“A uniform rule of naturalization” includes but is not limited to, who is a citizen - by birth or by naturalization. A citizen at birth is naturally born a citizen.
Yes, that is your rule. The constitution empowers Congress to make all newborns in the whole world NBC by declaring them to be citizens at birth.