Never determined that your interpretation is the one binding on the courts because no case has ever been heard challenging the Natural Citizen clause. "Citizen at birth" is certainly a more stratight-forward interpretation.
Suprem Court says differently, from Minor v. Happersett:
” according to the court, “it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners.”
I do not need courts to tell me what a natural born citizen is. I have known since I was a child.
The natural born clause was, and always will be, about divided loyalties at birth. Obama, Rubio, Cruz, non are qualified, and no “citizen at birth” is not the same as a natural born citizen.