i haven't heard this but then i haven't been paying a whole lot of attention to it since we're members of a conveniently located range.
however, i do know these few things:
cities and towns can have there own ordinances prohibiting shooting in the desert. scottsdale, for instance, does not allow shooting in the desert (just travel north on Pima and you'll see all the signs).
also, i think that shooting has been banned in the tonto national forest since sometime this summer. but i'm not really clear on that one, so you'd have to verify that with forest service personnel to be sure.
now, if ARIZONA passed a law that prohibited shooting in the desert, that would have been done by the state legislature and could easily be verified with a call.
fwiw, i think that the law sucks, if it exists.