gonzo,
"Try to imagine the integrity of play WITHOUT referees."
Way back when, I used to play competitive Ultimate (a really cool Frisbee game for those of you unfortunate enough to have never played). In the official rules of the game, there is a stipulation that there will NEVER be referees or officials. From weekend pickup games to the World Championships, the players call their own fouls. This tends to be very self-regulating, as abuses of the system are quickly dealt with by the players. Maybe it's part of the "hippie" culture associated with tossing a Frisbee around, but I've never seen real unsportsmanlike behavior during an Ultimate game.
Maybe more sports would benefit from not having referees, and letting players be responsible for the integrity of the game.
But then, who would the parents yell at?