Not quite. According to Wikipedia, Joe South wrote the song for Billy Joe Royal, who recorded the song before Deep Purple.
In the case of Jagger/Richards, I believe Ride On, Baby was recorded first by some pretty boy singer (checking Wikipedia) some guy named Chris Farlowe. Not a very impressive recording, though.
I seem to recall that there were several Lennon/McCartney songs that were recorded by some of Brian Epstein's other clients.
(dammit, now I'm thinking about that gag in that one episode of The Comic Strip Presents, where a guy named Keith Epstein steals a demo tape from a recording studio he's making a delivery to. He later makes an appointment with a recording executive who asks him if he's related to Brian Epstein. Keith says, "Yes, he's my...brother", lying of course. The executive pulls out a little notebook and says, "Congratulations. You are the...34th brother of Brian Epstein I've met since taking this job")
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