If you look up the Nationality act of 1952, the title of the section which makes a citizen out of a child born in a foreign country to a single American parent is "Naturalization by class."
In other words, the act regards the citizenship of foreign born children of one American parent as a "naturalization of a class of people."
The Supreme Court agreed in the decision "Rogers v Bellei", in which Aldo Mario Bellei was deemed to have lost his citizenship for failure to meet the residency requirements outlined in the statute which bestowed citizenship upon him at birth.
In other words, such citizens have statutory, artificial, man-made conditions placed upon them. (because they aren't natural citizens.)
Natural born citizens do not have any conditions which they have to meet in order to remain citizens.
All of them except Santorum would fall under the provisions of the Immigration and Nationality Act of 1965. Under that they're natural born citizens.