I don't think this is too crazy. I wanted to work out in the gym, but my parents would only let me do cardio equipment until high school. Every time I mentioned weights my dad would say i had to do some random number of push-ups before I could...and the number would magically increase the more I could do...but the fact that they desire to be in the gym isn't new.
I'm no doctor and won't pretend to be...but if people under 16 are in the gym, they should be supervised. At the very least they can mess themselves up with bad form. It'd be difficult for some districts, but ideally there would be some program at their schools where a coach can help them develop correctly.