Most of the places I camp in both the Gila Wilderness and Lincoln National Forest are very remote. There is usually no cell service, and there may not be any law enforcement presence for 40+ miles in any direction. That means that if you chose to camp in these areas, you are responsible for your own safety....which, in reality, you are anyway...regardless of where you are. 99% of the time, law enforcement investigates crime after it happens...they don't prevent it. They are a miniscule percentage of the population, and they can't be everywhere. So it behooves one to both accept this reality, and prepare for it.
Ironically, when I'm in these places, I rarely feel any out of the ordinary threats. There are threats, of course, like wild animals....there are things like lightning...and of course I could have a cycling mishap...but it would be extremely rare to have a 2 legged threat. It's places like the OP mentioned where you are the most vulnerable. Do all you can to negate those threats. Above all, never underestimate your opponent.