Actually, not wrong. Words matter. Ask all of those who correctly assert “born citizen” is not the same as “natural born citizen,” which would include the Constitutional Convention. The Constitutional Convention rejected Alexander Hamilton’s draft of “born a citizen” and adopted John Jay’s “natural born citizen” for Constitutional eligibility for POTUS.
There is no proof that Hamilton's language "born a Citizen" was ever submitted to the Convention. The Convention couldn't reject what it never read.