The Beatles did launch their careers playing black music for white people, but after a short period of playing covers, they went on to some really innovative composition. I keep a playlist called Pairs, which is made up of songs that somehow go together. Many of them or Chuck Berry/Beatles, Little Richard/Beatles, and so on. Listen to the Isley Brothers' version of Twist and Shout alongside the Beatles'. Ron Isley has a more comfortable vocal range, but John Lennon really put some lift into the tune. As dvs0416 says elsewhere here in the comments, the Beatles were open about their influences. See if you can find the video of Paul McCartney talking about how Jimmy Hendrix detuned his guitar with a whammy bar in a club one night and was trying to see past the stage lights out into the audience so he could find Eric Clapton to ask him to come up and help Hendrix retune. It was all affection among them.