Meh, “natural born citizen” is a term relevant only for the Presidency, and nothing else, certainly not for cabinet posts, which have no citizenship requirements at all. Cruz could be the Prime Minister of Canada and still hold a cabinet post (though he probably wouldn’t get through Senate confirmation!).
Right, did I say otherwise? I mean, the U.S. Constitution states the requirements quite plainly. The POTUS is required to be a "natural born Citizen" post grandfather clause.