It's probably bollocks but there still might be a bit of truth in the story.
Alves is 29 and his form has completely detoriated since the second half of last season. Something is obviously wrong with him for a while now. Complacency? Past his prime? Who knows. What I know is that he's our worst fullback this season by far. While at the same time Montoya is a huge prospect ready to step in. From a footballing point of view I wouldn't find it unreasonable even now if we could cash in for him. He's on huge wages (almost Xavi and Iniesta level) but doesn't provide THAT much more than Montoya nowadays. His best times are behind him not ahead of him. He will definitely not stay here for 3+ more years anyway with Montoya riding the bench.
Villa will be 31 soon and he's coming back from a leg break. Nothing to do with his attitude or performances but Pep might have seen Sanchez as the long term replacement and wanted to make room for Sanchez, simply because of age reasons.
Pique is the biggest celebrity in this squad who's obviously not always focused on his football. A very un-Pepish footballer actually. If he weren't from La Masia, he'd definitely be gone for the attitude he's shown last season.
Cesc. I don't know. Maybe Pep realized that he isn't a Barcelona style midfielder. Maybe it was his attitude. Maybe he realized Thiago was a better option for the future?
It would have been a huge change of the team and dressing room dynamics but that's maybe exactly what Pep wanted to keep on winning. Something new. This is the same guy who got rid of Ronaldinho, Deco, Eto'o and Ibra after 1 season. Does it seem that unreasonable that he might have wanted to replace Alves with Montoya, Pique with Hummels or Bartra or Muniesa or Mascherano (Puyol and Mascherano played the most together last season after all) and sell 30 year old Villa + Cesc? It's probably bullshit but if someone asked me which players Pep would sell if he had to, Alves and Villa would top the list IMO. And if someone asked me which player is the most un-Pepish player attitude-wise, it would be Pique.