Just how important is Chauncey Billups to this Pistons team? He was the only Piston this season with a PER over 20 (sorry Watson, Amir Johnson doesn't count) and is a premier defender at his position. Most importantly, Billups leads the team and is usually the guy with the ball when they need a score, and that score often comes from the foul line.
I'd go on, but Justin Lyons at NBA.com does a nice job going over how the switch of Hinrich on Billups may have helped derail the Pistons. Even if Chauncey doesn't get in foul trouble like he has the past couple of games, merely slowing him is a big step towards slowing his team.