Stanley you are half right. It is illegal for EVERYONE to use a motorized vehicle to locate (hunt) animals in the state of arizona. The champ permit you are thinking of allows those to shoot from a motorized vehicle but they still have to be OFF the road when shooting. It does not allow them to drive around looking for animals.
And as Packer said, most of the roads south of 260 are "technically" closed for travel, even some with numbers. 99% of people do not know this rule even though there are big brown signs on almost every major road coming off of HWY 260. Its just that nobody reads signs or dont care.