It was probably nothing more than Billy just never being needed for the tribute concert.
Billy is not a big enough name to merit an involvement in the event. Rick was only a part of it due to his reverence of Peter. It also sounds as if it was a peace offering from Mick to Rick as they'd fallen out a couple of years previously (or at least grown apart).
All other guitarists involved were A-listers or iconic players. Billy wouldn't have added anything.
I'm sure it would have had nothing to do with Stevie Nicks' opinion.

Do you not remember all of the various Boston Tea Party comps?

If it has the Fleetwood Mac name, there will be exactly that Manchurian Candidate level of intrigue and plotting.

Lindsey did a round of interviews in 1981 for his first solo album. He revealed a number of interesting things about the album. Mick’s drum track is a loop, like “Tusk.” They couldn’t get a satisfactory full drum track from Mick, but they got great patches. So they took fifteen or twenty seconds of a patch, cut the dioxide tape, glued the end of it back to the beginning, and then ran it through the player to create a full drum track. Lindsey said that the result still had Mick’s signature creep (drum style).