Ah, but the difference is that Rod *could* have played on it, because he was a session musician in London at the time. Rod's theory was that the story came about because there was another session musician around at the same time who looked liked him, and it was an honest case of mistaken identity. Though I think that theory was based on it being someone other than Pete Hogman.
The other difference is that while the Bob Holness story is often bandied about as a "common misconception", you'd be hard-pressed to find anyone who ever actually believed it was true - it seems more of a common myth that it was ever a common myth! Whereas the Rod Stewart story really was widely accepted as being true for many years.