Umm, the good doctor's wealth comes from HCA, a chain of for-profit hospitals that once held the record for the largest fraud settlement in US history. Frist clearly has excellent PR, because very few people ever mention this.
Frist makes sense on the board in that he definitely knows who to call at the FDA and would get his call answered. As unsavory as it is, lobbying experience is valuable in tightly regulated industries. I have no idea if he's a good doc, or the ethics of HCA, but from a purely pragmatic perspective, of all the names his makes the most sense on that board.