Congress has no power to define who is or is not a natural born citizen, for purposes of Art. II sec. 1. Changing the definition would be changing the Constitution. They only have the power to make a uniform rule of naturalization.
I don't know if they realized that when the changed their 1790 law in 1795, to read "citizen" instead of "natural born citizen" or not. But it seems possible that they realized they had overstepped their bounds, and moved to (quietly) correct the error.
This about it, if they could change the meaning of "Natural Born Citizen", unilaterally, they could change the meaning of "freedom of the press", "freedom of speech", and of "arms", just as easily.
That's not to say they could not pass Constitutional amendment defining "Natural Born Citizen", but that would need to go through the full ratification process and be submitted to the states for ratification.
The best quick synopsis of the issue with links to supportive material.
Bookmarked for reference.