DM fiat is both a right and responsibility - it's a right in the fact that as the DM, you have sacrificed your time to run a game for everyone else, you are trying to run an enjoyable and cohesive game, therefore you have the right of fiat.
On the other hand, if you consistently pass down bad or unfair judgements, expect players to get unhappy very quickly, and start leaving the game soon after that.
In my own group, we all acknowledge that the DM has the right to make a final decision. We are free to ask why, or to offer suggestions that perhaps he hadn't thought of, but if the decision stands, we abide by it. Outside of the session, we all feel free to discuss rulings and say whether we thought it could have been handled better.
The one thing we all want to avoid is bickering and rules disputes during a session. To this end, we are all prepared to accept a DM ruling, even if we mightn't agree with it.