You're correct, the Arizona Gray Squirrel lives in canyons in mountainous areas of eastern Arizona and western New Mexico. It is not known to occur in the Phoenix area. Although I know of no populations of nonnative squirrels in the area either, I'd say it's more likely, based on the habitat and behavior, that it's an Eastern Gray Squirrel, which is only slightly smaller. Many individuals of this species have been released in cities all over western North America. Let's hope this one isn't the first of many.