I would contend that because it's a sport with legalized betting, the stewards (the referees) at horse races are the most transparent (call it honest). The setup is such that everyone in the game knows how it works and the room for knavery is pretty small.
Tracks have high-speed video cameras watching the race. The cameras are high enough to see down onto the pack and catch illegal moves or even the whips as they fly during the race. The stewards get a really clear view all the way around.
And the jockeys are quick to claim interference. They know they have a chance of making it stick with all the video footage. Sometimes it seems like they're taking a flop in the hopes of improved placement after the call but who knows.
The key is that the stewards are not at all hesitant to hold up the announcement of the final order of finish. There's half an hour until the next race and a little anticipation never hurt the race fan. The track can play back some of the video for all the arm-chair judges to see for themselves. And the call gets made.
The system is so intrusive that blatant fouls are rarely worth the trouble and too easily caught. But it doesn't interrupt the flow of the race (for better or worse).
I'd vote for racing stewards as among the best referees around. And I'd say that the nature of the sport makes it about the easiest to ref.