The Beatles never pretended to be a blues or rb band, and their covers of black rb hits were their worst recordings. They could have skipped any of their covers of blues/rb recordings (Matchbox, etc), and it wouldn’t have affected their popularity one bit. That’s all right, I never for once thought the Stones sounded black either. I liked the Stones because they had a unique sound, that’s all. They could do songs like Angie as well.
They didn’t exactly sound black. As kids from a different musical culture, they absorbed what they could from black music and made their own sound. Music being music, it doesn’t fit into the descriptions and neat categories we try to make for it. It just flows along.
Re the “stealing” issue: I do remember really hating the white covers of black songs in the fifties that took a song with an exciting spirit to it and made it into a white piece of junk. “Dance with Me Henry,” “Tweedly Dee,” etc. The names Georgia Gibbs and Pat Boone come to mind. Happily, that trend was short-lived.
Then of course there was the other kind of stealing, “with a fountain pen,” as Bob Dylan says in “Talking New York Blues.”