You’re confusing citizenship with Natural Born citizenship which is declared in the constitution for the office of president. It is based on allegiance, and freedom from foreign ties.
No, that's not correct. You are only repeating the starting point for this debate. It's the thing in dispute.
"Natural born citizen" simply means someone born a citizen. The stuff about two citizen parents and being free from foreign ties, has nothing to do with it. That's what people have been trying to argue, but they have nothing to back it up with.
Citation?