In mediation, there are no "adverse parties", rather than "participants". This is a crucial difference. You and the other person(s) facing the disagreement will not only be able to actively participate and to contribute to finding solutions, but this is actually a necessity (as the mediator will not "decide" for you, see above).
Hence, if you expect the mediator to judge according to "truth" or "rights", then mediation is clearly not for you.