Evidence is watching the game and seeing how many stupid calls the refs make to help one team win. If one team gets away with more fouls without them being called, they will foul more. If one team can violate the rules more without getting called for it, they will do those things more, and gain an advantage, and it won't show up in stats necessarily.
Furthermore, if one team doesn't get the call when they are being fouled, and the other team does, this can cause exactly the discrepancy in turnovers that you refer to. What you think is evidence against my conclusion is actually evidence in favor of it.
Plus you have to watch to see things that don't show up in stats, like miscalled out of bounds plays, goaltending, etc. Which team gets to travel all over the place, and which team gets called for every possible violation of 3 seconds or whatever?
There was one stretch when the Lakers built up the lead, and the refs blew the whistle every 15 seconds it seemed. A third of those whistles were bogus calls against New Orleans. That's the difference in the game right there, not even counting all the calls in the rest of game.