Wow! I remember running up the canyon that was uphill of the main (original) parade ground when I attended the Military Intelligence Officers Advance Course back in 1982. A lovely quiet place to run back then.
Huachuca Canyon is still in pretty good shape for running, and has very little illegal alien or smuggling traffic. The MPs have a worse reputation than the BP officers, whether it's deserved is moot.
However, the canyons leading out from the tank gunnery range (Garden and Woodcutter's) are prime routes for illegals. They hit the highway for rides north about a half mile from my house.