I think it might be Billups idea to sit the Birdman for game 4. Why? Well I was reading this article
ESPN - OTL: The Disposable Superstar where there was an incident with Carmelo where he refused to come out during a game with the Pacer. The front office in Denver suspended him but as it turned out it was Billups idea to probably teach Carmelo discipline. The Birdman was out of control during game 3 on Saturday. There's probably no food poisoning whatsoever and Denver probably didn't want to get press for benching one of their top player during the Playoff.
Am I paranoid? I don't think so. I wished Billups had influenced the front office in Detroit to bench the whole front line during a couple of seasons when they weren't doing their job.