> with the exception of Frist a quick read shows no connection to healthcare
Well, there's also Shultz, who was "a director at biopharmaceutical company Gilead Sciences," according to this article.
But you're right that those people are mainly on the board for their influence in Washington. The importance of that when taking on an entrenched and heavily regulated industry can't be overstated.
As others noted these board members appear for another purpose such as government issues or attracting others by the halo of their importance.