Only if you think a natural born citizen and a citizen at birth, are different things. People born of two US parents, or one parent that meets the US residence requirement, are citizens at birth. Including McCain, not including the Anointed One, if he was not born in the US.
This has never been adjudicated. The first law, passed in 1790, on such issues, declared:
And the children of citizens of the United States, that may be born beyond sea, or out of the limits of the United States, shall be considered as natural born citizens."
So it seems the first Congress, comprised of many of the same people who wrote the Constitution, which was ratified a year earlier, disagree with you.
I'm recalling that this language from 1790 was modified in 1795 to read "... shall be considered as citizens." This would mean an intentional distinction from natural born citizens.