I've never thought of *any* part of the GMing process as arbitrary.
A human being is deciding what happens next. A human being is deciding what the opposition will be, and what the consequences for failure will be.
A human being is deciding whether to adjust dice rolls behind the screen or not. Reduce damage the orc did to your PC or not. Have the orc change targets to the Paladin, because he darn near killed you last round.
Now we can eliminate really dumb or ridiculous things the GM could do as bad DMing and not part of the scope of the discussion.
Within the scope of decent GM behavior, there's a lot of leeway for the GM. Your PC succeeds because the GM chose to not put an insurmountable barrier or consequence in your way after you kill that cop while robbing the bank. The GM decides the bounty hunter exists and that he has enough resources to collect info to hunt you down, and just happens to arrive to capture you after your big boss fight when you are down on resources.
When a GM says they enforce consequences for PC actions, or "no good deed goes unpunished" they are exercising the same arbitrary force a police officer has when he decides to give a warning rather than write a ticket.
When considered from the all-power of the GM, as players, we are at their mercy and trust them to render a good challenge and fun game. And in that context, worrying about the honest of the dice rolls is like calculating the total mass of the universe without taking into account Dark Matter/Energy.
Dice rolls is the least of your problems as a player. It's like getting mired in office politics over how many photocopies you used up when the goal is to sit in the big chair made of swords.
So a player cheating next to you in D&D may have SOME impact on you within the game or emotionally. But there's no real money on the line, and it's generally all the players working together versus the GM. Your fellow player cheating is not as large a problem as your GM doing a bad job. When he kills an extra orc because he cheated, the party is closer to victory, and that's one less orc that could have hit you.
Thus, the odds don't matter in an RPG the same dramatic way they do in Poker. Players in D&D (unlike WoW) aren't usually measuring their next action based on DPS or % chance of the GM rolling a 19 (unlike poker, where your decision to fold is largely based on the % chance you have the best hand or will draw a card to get the best hand compared to the % you have to pay to stay in the hand).