... and who pray tell, is to tell us what a "natural born Citizen" is? Of course The SCOTUS is empowered to enforce absolutely nothing. Its constitutional task is to take appeals and decide them by interpreting the Constitution.
Suppose a candidate's eligibility were challenged by Congress and they declared him ineligible. How would that candidate appeal that decision? Yes only Congress can enforce the rules of the 20th Amendment, but only The SCOTUS can interpret the meaning of the Constitution and its Amendments, when properly asked.
In order to decide which of us is correct, The SCOTUS would have to accept an appeal, or let stand the verdict of a lower court. In the specific instance of defining "natural born Citizen" in regard to the candidates now under discussion, they have done neither.
Minor versus Happersett is already precedent - Born on soil to Two citizen parents. This either is or is not the condition of the President Elect.