Yes, there are many pitchers who change up the arm slot to give a different look. I do think that there is a slot that is most effective for each pitcher though. I'm not so sure that it's as cut and dry genetically as House would claim, as people like Paul Nyman seem to be proving that they can makes certain guys' arm action better.
When you talk about Bagonzzi saying that "how high the elbow is above the shoulders" determines arm slot, are you disagreeing with him. It would seem that he means that the relationship of the elbow to the throwing shoulder determines arm slot. You've already proved that most guys do throw with their elbows below both shoulders.