Incorrect. He is a libertarian. He is not a Libertarian. He is a Republican. He may be a republican also.
I am a Libertarian, and a libertarian. I do not support open borders. Your conclusions are incorrect, as is your logical methodology.
It was pointed out to me that Ron Paul is a card-carrying member of the Libertarian Party. The person who pointed that out to me thought that made him a Libertarian...as well as a libertarian. In my mind, that's a tough call. But I'm sure he's REGISTERED as a Republican...so I tend to agree with you that he's a more of a libertarian than a Libertarian.
Mark (Libertarian and libertarian)
P.S. And (of course) I support open borders (no numerical limits on immigration). As a Libertarian (and a libertarian) I understand that a person owning one piece of land does NOT give him any right to say who may own the adjacent piece of land.