I remember a long time ago that someone had claimed that Paul was such a workaholic, and he performed in every single song with the exception of one.
I don't know how valid that is (it seems plausible), but for whomever posed that question, Within You Without You featured George and other musicians, but no other Beatles, including Paul.
There were a number of songs that Paul didn't play on -- for instance, just check the White Album, beginning with Good Night and then Julia. By the same token, John wasn't on every track either. A good source for this kind of info is "The Beatles Recording Sessions -- The Official Abbey Road Studio Session Notes, 1962-70," by Mark Lewisohn, with introduction by Paul.
As for She Said, She Said, all four Beatles were present according to the same Lewisohn/McCartney source.
"John brought it into the studio pretty much finished. I'm not sure, but I think it's one of the only Beatles records that I never played on. I think we'd had a barney, or something, and I said, 'Oh, f*** you!' and they said, 'We'll do it.' I think George played bass."