Just to be that robot, but the actual text in Article 2 is:
No person except a natural born citizen, or a citizen of the United States, at the time of the adoption of this Constitution, shall be eligible to the office of President; neither shall any person be eligible to that office who shall not have attained to the age of thirty five years, and been fourteen Years a resident within the United States.
Now whether "natural-born" means "born in the country" or "born a citizen [wherever]" is apparently still being debated, but regardless the citizenship requirements for president are still more than just "naturalized." (which would include anyone who has immigrated)
And just for the bonus lulz, the questioning types included such fringe figures as... NBC news. (in this case, towards Ted Cruz)
It's not settled, because the Constitution does not define "natural born," a phrase that appears in the nation's founding document only once.
www.nbcnews.com