Well I could be wrong but I believe they do have the rights to Sun, also to Vee Jay.
I don't have definitive information on this but they have been issuing Sun material for many years, you would think someone would have noticed by now. Also some of the Sun and Vee Jay material they are issuing is NOT public domain. e.g. a recent release of Jerry Butler singles of Vee Jay material.
I don't have the Rich set but I have a similar Johnny Cash set. The label states that the recordings are licensed from Sun Entertainment Corporation.
What they don't have, and got into a lot of trouble for, was Chess.