Show me where it defines naturally that way.
When one is born in this country of citizen parents, one is naturally a citizen as it is not possible to be anything else.
Anyone born something else is not naturally an American.
That is what natural born citizen means.
The rejected “born a citizen” as too vague. (Hamilton’s suggested phrase)
They wanted a higher standard that would guarantee no foreign influence on that one office. (see John Jay’s letter to Washington)
Thomas Paine opined that we would never half a “half-foreign” President unlike the English who had German Kings because of the natural born citizen clause.