I've contacted the BLM for info (they didn't provide much) but I thought I'd cast out here too...how's the camping at Box ? toilets ? tables ? shade ? electricity ? crowds ? (apparently they don't take reservations).
It's not really a designated campground, but I think it is on BLM. Have not seen many people camp out there but I have personally done it with no problems. I have never seen any no camping signs out there so you should probably be just fine.
Supposedly you're not officially allowed to camp in the SMA, but I think they fixed that in the RMPR, though I cannot find it. There's not much in the way of a nice campspot, like mentioned earlier it's rocky and often windy, no shade, there can be a lot of people trying to park in your campiste to get to the rocks. Just South of Box in Black Canyon is a much better spot, just past the Major Wall/Unbeatable parking and yellow cattle guard. The rising sun hits it and the view is nice. Officially, this is State land but no one seems to care.
A real nice campground is Water Canyon, about 10 miles West of Box up in the Magdalena Mountains. It's a brand new Forest Service site, just been refurbished, free, toilets tables tent spots shade trees, usually few other people, but (like box) no running water. You can filter water out of the stream, but it's better to bring it.