Andy, didn't the Stones version use the same backing track? If so, does that mean the Stones provided the backing on the Chris Farlowe's single version (in addition to Jagger/Richards on backing vocals)?
The musical backing to Farlowe's finished version was the demo track The Stones used, whether that counts as the band 'backing' Chris Farlowe depends on your point of view - or whether you're a Rolling Stone or Chris Farlowe!