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Not necessarily. Under the citizenship and naturalization laws that were in effect at the time of his birth, his mother would not have been old enough to confer U.S. citizenship to him if he was born outside of the United States:

http://www.greencardlawyers.com/citizenship/citizenbybirth.html#Chart%20to%20Determine%20Citizenship%20Rules

Close, but I believe not quite correct.
To be a Natural Born Citizen, both of one’s parents must have been American citizens at your birth (plus you were born in USA).
A person born of one American citizen parent (as you cite) is usually considered to be an American citizen, yes, you are correct on that score.

(note: this is a different category than the Natural Born Citizen as required for eligibility for the presidency) ...

Also, this citizenship for the child is not universally the case ...as it is governed at least in part by certain statutes ... For instance, I believe reading that if someone is born outside USA to an American parent who is statutorily unable to pass his or her citizenship along to the child, such as someone like Obama’s mommy at the time? ... since she was reportedly not old enough to meet the statutory test then in effect ...?, then the child does not acquire citizenship at his birth....but anyway I was speaking to the Natural Born Citizenship issue above and that’s far more than sufficient for us now.)

ps: I think that takes care of it... I do need to sign off now .... so maybe somebody else can kindly pick up the ball and advance it forward for us all here now? Thanks!
Thanks!

One who is born of an American citizen is considered a natural born citizen.

This is correct.

Birthers can scream from the rooftops all they want. Nobody's buying their made-up definition of NBC that requires both parents to be U.S. citizens.