I have given you my evidence from the Constitution. Kindly give me yours.
Your definition is incorrect.
If it were the case, Obama would not be President.
There is also historical precedent that Natural Born Citizen means being born, and not naturalized, in the US.
The first presidential nominee of the Republican Party, in 1856, was John Charles Fremont. He was born in Georgia to an American mother and a French father. Jean Charles Fremon was born a French citizen, near Lyon, France. He was not a U.S. citizen at the time of his sons birth and never did become a citizen. Abraham Lincoln campaigned for Fremont. All the founders of the Republican Party campaigned for Fremont.
So, we have strong historical precedent.