There's some liability aspect to it as well.

These conditioning workouts are intense; there's the story from USC a few years ago of a student-athlete dropping a barbell on his neck. Add to that no access to your athletic trainers or direct contact with your strength coach who can make adjustments needed to account for injury (for example, someone has a sore shoulder, how do they adjust lifting). Absolute worst case is a kid drops, needing CPR or an AED during a workout, with no one near by.

These conditioning sessions aren't your typical head to the gym and run a bit on the treadmill thing suburbanites do.