You just contradicted yourself. If you're born a citizen then it happens at birth. You can't retroactively grant someone natural-born status. If Jindal was born here then he became a citizen at birth. You have no say in the matter. You're not the arbiter of who is a natural-born citizen and who isn't. The 14th amendment states that individuals born on U.S. soil are U.S. citizens. There are only two types of citizenship, regardless of what some on here think: born and naturalized. Jindal wasn't naturalized so he must have been born a citizen in Baton Rouge.
You are conflating “citizen” with “natural born citizen.” The reason for the clause in the Constitution was the desire of the Founders that anyone with allegiances other than to this country should not be eligible. Conservatives are like liberals in this. They want strict rules followed but not for their own guy. I think the law actually on the books says there needs to be at least one born citizen parent.