That does sound interesting, but the only thing is that if the two refs have two drastically different outcomes for whatever reason (also, what about things like, say, thunder rolling a hit for one ref but a miss for the other?), the same moves may not be logical in both situations, and asking both trainers to use the same moves would be a bit more... "staged", I guess? For example, if both Darkly and I were going to ref it and someone's Pokémon was almost out of energy, that player would be forced to stop and relax if they didn't want to lose under my reffing while they could theoretically continue to attack under Darkly's and worry about the forced relaxation later.

Now, aside from things like accuracy/crit/effect rolls, etc., I don't know that most people's interpretations of attacks and damage scales would vary that greatly, but should it occur it could create a situation where people would not issue the same attacks in both battles.