“What were the rules”
The term “natural born citizen” is not defined in the Constitution or the US Code.
Birther bluster to the contrary, there are no precedents which are on point.
If the certificate is not a forgery (which, by now, would entail “a conspiracy so vast..”) it proves Ann Dunham’s child was a US citizen by birth, that he was given the last name “Obama” at birth, and that his father was not a US citizen.
Unless the definition of NBC can be litigated to the point that the “2 citizen parents” concept becomes valid US law, or this document can be proved a forgery, it’s over.