Another thing I just remembered is steals. Teams that have guards that like to hack away for steals on the perimeter are more likely to pick up a lot of fouls (and get into the penalty early). Look at the Pistons:
Billups: 0.82 steals per game
Hamilton: 0.66 steals per game
Prince: 0.69 steals per game
That is easily the lowest of any team's 1/2/3 players combined.
Again, I'm sure the Pistons get some beneficial treatment, but I don't think the dicrepancy is nearly as big as the numbers look. There are other reasons.