Quote: we went to a mediator not an arbitrator. Don't know if that makes a difference
P.S. don't know if this was already answered for you, but a mediator is definitely different than an arbitrator. You are correct in that in mediation, the parties are mainly working together, with the guidance of the mediator, to come to a amicable resolution. The mediator is basically the guide to this resolution. An arbitrator, on the other hand, is more like a judge in that, while impartial, will listen to both sides and make a determination as to the result. The parties do not come to an amicable resolution on their own.
For what its worth.....
"Achieve success, but without vanity; Achieve success, but without aggression; Achieve success, but without gain; Achieve success, but without force." Lao Tzu