Since you are going to be in an environment that does have scorpions, there is always the possibility you may get stung. I also cowboy camp frequently below the rim and have yet to get stung. A lot of it is luck, whether or not they get you. But take some simple precautions like shaking out your gear, including your pack, anytime you set it down. If cowboy style, wait to lay out your bedding until shortly before you plan to go to sleep, gives the creepy crawlies less time to make it home. Check your footwear thoroughly before putting them on, etc. Also, check before you sit, look on and under picnic tables, benches, etc. I'm not surprised someone got stung sleeping under a picnic table, they should be thankful it was a scorpion and not a black widow. And the comments about mice and ravens are right on. Use the ammo boxes and don't ever leave food sitting out, even for a short time. I once saw a raven fly overhead carrying a full size bag of Cheetos. I wish I would have gotten a photo of that!
Just out of curiosity, what is your itinerary?