Actually, that's not in SW Arizona. It's considered to be in SE Arizona, since it's a little east of center.
SW Arizona would be the Yuma area, or Barry Goldwater bombing range (permit required), or Cabeza Prieta National Wildlife Refuge, Muggins Mountains Wilderness, Imperial Wildlife Refuge, Kofa Wildlife Refuge, etc. It is very dry desert out that way, unless you are directly on the Colorado River. I love it, but some people find it to be a bit too intensely stark.
On the other hand, if you want an off-the-beaten path campout in Southeastern Arizona, try Cochise Stronghold in the Dragoons. There are many places to car-camp which are kind of away from the tourist path, of course, but that one just popped into my head. There's a quiet campground at this trailhead, at East Stronghold: http://hikearizona.com/decoder.php?ZTN=759