Correct. Rubio is a 14th Amendment citizen. He has the same citizenship as a naturalized citizen. They are not eligible to the office of President. (All anchor babies have this citizenship. Are they eligible?)
Vattel stated in 'The Law of Nations', which the founding fathers used (even stating the Law of Nations in the Constitution), ' a natural born citizen is one whose parents are citizens of the country.' THAT was the definition when the Constitution was written. It isn't explained in the Constitution because everybody knew it.