Supposedly the host on the black radio station said, with great dry wit, that the charges were unfounded and unfair, that most blacks weren't going to believe it, and that it wouldn't hurt Hank Jr.'s record sales in the black community.
Hank JR has done a lot of questionable things in his life but I would say being a racist is likely not among them. Another possibility is another patients family making the call out of spite thinking they were getting prefered treatment in the way of testing etc. I doubt anyone believed the rumor to start with. Politics may have had something to do with it to. There's just no telling.