I would imagine that the rule is in fact no non copper plated bullets, and you may be reading it wrong. Of course I could be wrong.
The typical reason for this is to reduce lead exposure by vaporized lead bullets through only allowing bullets fully enclosed with copper to be shot.
It really doesn't matter much in reality for most pistol rounds except for high velocity ammo that vaporizes more in the bore.
Plated, FMJ, it should be all the same for such rules, the lead is not engaging the bore, so there is no real lead vaporization.
If in fact you were correct in your understanding of no plated rounds I cannot understand a real reason why they would differentiate with jacketed, except perhaps to force you to use their own marked up ammunition. There is a minority of ranges that want you to buy and use only their own in house ammo, which is typically marked up significantly and so works as a major source of additional income. A sort of hidden cost that can actually make lower range rentals a much higher price than another range that charges slightly more without such a rule.