Yeah, heard that story of Brown and the Stones. I don't think anybody touched him on that show. He was superb.
I guess it difficult to follow a genius especially if all you have to offer is American Blues music performed by a load of middle class white guys from England. 
Then you better lump in The Yardbirds, Who, Clapton, Jeff Beck, Led Zeppelin etc., with the Stones too. Probably half the "British Invasion" were White guys playing American Blues music.
Truth is, a lot of those Blues guys benefited from the Brits "ripping off" American Blues music, they had late life 2nd careers playing the UK after their popularity fell off in the States...