When I did a coaching program for Judo (NCCP Level I, to be exact), I was taught to never allow pre-pubescent children to do strength training. Callisthenics are okay, because the resistence is limited by the child's body weight, but weightlifting of any kind is not. Something about building up too much muscle around the joints, leading to arthritis later on.

EDIT: I just went looking for sources for this, and I cannot find any. Unless someone has better Google-fu than me, take what I said above as an extremely suspect anecdote. It seems that the major risks are that coaches will push children too hard, causing damage to muscles, tendons and so on.

He doesn't lift weights, just push ups, squats, jumping jacks, etc.

there's also an issue of Rhabdomyolysis http://en.wikipedia.org/wiki/Rhabdomyolysis