There are tons and tons of songs that are cover versions that people think are originals but have been nicked from way way back in time. It is in common practice for virtually every mainstream artist unless they use only stuff written especially for them either by their own hand or someone else.
For example. I Heard It Through The Grapevine was originally recorded by Gladys Knight and the pips in 1967, then it was recorded by Smokey Robinson & The Miracles in 1968 and then later on in 1968 the Marvin Gay version was released on the album "In the Groove" and then was released as a single. So what most people think is the original version by Marvin have got it wrong.