Naturalized!!! See how easy that is?
Responding with;
The law says that such persons shall be citizens at birth.
It does not say in that portion of law that such persons shall be naturalized at birth.
Yet that is what you are arguing, importing the assumption that all persons born under conditions of that heading and paragraph (g) are somehow being "naturalized" by the statute, rather than the "shall be nationals and citizens at birth" is addressing deriving citizenship from a U.S. citizen parent when in circumstance of being born abroad.
Sorry, but the laws are as written (in whichever applicable era/time frame -- and those laws have changed, repeatedly) not some other way (applicable to whichever era/time frame).