Leiber and Stoller wrote Hound Dog for Big Mama Thornton; thet didn't appropriate her version of it.

Joe Turner's "Piney Brown Blues" ("Well, I've been to Kansas City...everything was really all right") is similar to the song Leiber and Stoller wrote for Little Willie Littlefield, later covered by Wilbert Harrison, in that they both use the words "Kansas City." Outside of that, there is no resemblance in either words or tune. But why stop there? There have been lots of songs written about American cities, and certainly a lot about Kansas City. There's Joe Jackson's ("Walked up Tenth Street and I walked down Beale/Tryin' to find that gal that they call Lucille/She done moved to Kansas City...") There are lots of other songs about women named Lucille, too, but that doesn't mean they were all stolen from Joe Jackson.