Congress, as established via Article I Section 8 of the constitution has the full authority to established the rules of naturalization. While that does include your statement above, it includes far more.
It includes the rules for who is able to apply for naturalization, what the ceremony must consist of and it also includes who is a citizen at birth and does not need to be naturalized, i.e. a naturally born citizen.
Some of those rule, in particular those who are born citizens, are described in Title 8 section 1401 of the US Code.
Your error is a common one, easy to make, and even tempting to make.
I am unmovable from my belief on this issue, and suggest that we just leave it at that, so as to not generate any expression of hostility here on FR, nor bad feelings toward one another aside from what we post.