Naturalization only applies to those who are not already citizens by birth.
"Naturalized at birth" is an oxymoron as far as citizenship goes.
Look chum, I dare you to go to the congressional globe and read the debates about the 14th amendment. You can see all the arguments made by all the different Senators and Representatives about why it is needed, and they get deep into the issues of what they wanted to accomplish.
If you do this, you will find out that Congress regarded the 14th amendment as a naturalization tool.
It set naturalization "at birth." And before you get started about "you can't naturalize at birth" nonsense, I advise you to read any of the naturalization acts this nation has produced, such as the Naturalization act of 1952, where it specifically says that these classes of people are being naturalized en mass "at birth."
Catch up to my level of research, and then get back to me.
Oh, and if you want a court case that revoked citizenship based on "naturalization at birth", check out Rogers v Bellei.