I've seen where some places forbid steel core or jacketed (even bi-metal, cause, you know, it sticks to a magnet), but, other than the laziness that was brought up, I don't see why steel or aluminum cased should matter. Heck, FM has steel-cased, coated in brass, ammo that has copper jacketed lead bullets, so that idea of all of it being steel core is definitely out the window (including all of the 7.62x39 I shoot, which has the bi-metal jacket, but a lead core).
The steel core stuff can potentially do some damage to a backdrop that isn't made for it. Not sure what a bi-metal jacket would do to it, though.
Maybe you should ask them. They must have a good reason.