He’s in Los Beatles along with Juan, Jorge, and of course Ringo
:: singing :: “and Ringo was his name - o.”
Just a shot, but… Free as a Bird and Real Love were written by John Lennon as a solo work and the others came along later and did a re-work of them. The Beatles had ceased to exist as a group in 1970 and they did not formally re-band, they just kind of jammed together (which they did several times on each other’s earlier solo albums without being considered The Beatles). Even if this doesn’t hold much water, most people only look to the “classic” years which ended in 1970 for true Beatles works. The Beatles without John Lennon would be close to Creedence Clearwater Revival without John Fogerty, it’s just not the same thing.
Pardon my total ignorance on this matter, and I hope I didn’t somehow miss it above, but…
Wasn’t there a song that was obviously kicked around by the Beatles but never released, then re-worked by both George and Paul for their respective solo projects? I think there was a lawsuit involved over the writing credits.
That would be Creedence Clearwater Revisited. They play around here all the time! 
(damn nice guys, too, despite what Fogerty says about them!)