It was because the 2nd congress recognized the error of doing so in the first naturalization act that they re-enacted the statute with the offending language removed.
Consider this - if you give me a list of numbers arranged in some pattern and ask me to "randomize" them, I'll return to you the same numbers in random order. If you present a foreign-born individual and provide a procedure to "naturalize" them, the result will be a natural citizen - with the same rights as any other natural citizen - which rights do not include the right to be Commander in Chief.
Foreign BORN, yes. If you are NOT foreign born, you are a NBC. In order to know who needs naturalization, you MUST define what a citizen at birth is. The statute does that.