I had heard the "Paul is Dead" theory that a man named Billy Shears replaced Paul in the band, but never thought anything of it, seeing as that whole "Paul is Dead" thing is nonsense. Furthermore, Paul introduces Ringo as Billy Shears (not himself), so the conspiracy theorists got it wrong anyway.
I had not, however, heard the rumor that Billy Shears was the man who busted The Rolling Stones. Keith Richards and Mick Jagger were first arrested for drug possession on 12 February 1967, and composition of "With a Little Help From My Friends" was completed on 29 March 1967, and recorded the same day and the day after. So the chronology does work out - it is at least plausible that the man who busted the Rolling Stones the first time was named Billy Shears. (Subsequent Stones drug busts occurred after the recording of "With a Little Help From My Friends" and therefore couldn't possibly have any influence on the song.)
Today, then, is Day 2, featuring "The Beatles: Band of the Sixties", my general overview of the band and their decade, at the Antioch Public Library District (757 Main St, Antioch, IL) from 7:00-8:30pm. I am told that 95 people have registered, which would set a new attendance record by 31!