The law says what it says. You can not read in what is not there nor read out what is there.
But that is exactly what you're doing.
You are reading in "naturalized citizen" or "citizen not natural-born" for "citizen."
The wording of the law itself does not specify whether the "citizen" is "natural born" or not. One has to conclude that by figuring out the intent.
Since everybody generally understood that anyone born a citizen was a natural born citizen, that's what it means.