There is an all-encompassing Section 138 by which you can ask an adjudicator to make a ruling on what the EC or Owners Corp should do.
If you go to mediation, then adjudication, the people who are pushing for this will have to show their evidence if they want a ruling in their favour.
By the way, their argument that you have to prove them wrong is nonsense. All you have to do is tell them that any decision they make that is not covered by the Strata Act will be a) challenged at NCAT and b) a ruling will also be sought to adjust levies so that they alone pay all costs.