Well the issue here is one of risk, 99.9% of the time there is no real danger involved in these games, and injuries will be relatively minor if they occur. The problem is that tiny portion of the time when a kid *IS* injured seriously, which of course opens the school to litigation, and if the school is receiving public funding in any capacity the state and town can be held accountable... through rising insurance premiums if nothing else (since if they have insurance to deal with this, the rates will rise once they have an incident).
It's a slipper slope issue, with no easy answer. The reflex is to point out that this is the result of the insanity of a legal system that allows people to sue for nearly anything ,people oftentimes forgetting how they would feel if their kid was seriously injured. There is also of course the connected issue of negligence and one of the big reasons why it's become possible to sue with enough of a chance of success in cases like this is that there have been plenty of cases over the years where physical education instructors HAVE been negligent, over the top, or were just not taking their job seriously which lead to the injuries. Removing liability from the equasion can also lead to a lot of problems.
One also has to understand that even when you don't get into punitive damages, simply having a school be considered liable for the injuries can be a big deal. I'm sure we all know people who suffer from injuries they sustained in school activities, especially later in life. When you get older some injury you seemed to shrug off playing football, falling down, or whatever else can come back with a vengeance or be the catalyst for various degenerative conditions. If some kid takes a bad spill playing kickball, and sprains their leg or something, and there are records of this where it's acknowleged to happen, this old sports injury could see the school having to pay out a lot of medical fees 20 years down the road if it can be tied to why some middle aged guy starts to have problems walking. You might laugh but cases like this have been won, and there is a lot of legitmacy to the central complaint, what's more if YOUR the one who is in pain, your going to want treatment and do whatever you have to in order to get it, and if that means going after your old school because you can't otherwise afford and injury like that, well that's what your going to do.
Don't misunderstand what I'm saying though, I think the situation is ridiculous, but I do understand it. Personally I think these schools and programs need to suck it up. Especially when dealing with private programs simply run through schools the things are cash farms. It basically amounts to a bunch of people looking to make some extra money teaching a few extra gym classes as a fancy form of day care, and charging crazy amounts of money for it at times.
The kind of thing they seem to be talking about is say where a Gym teacher gets permission to use a blacktop or school gym after hours (perhaps in exchange for some kind of write off the school gets for donating it or whatever), and then accepts money from parents to keep their kids busy for a couple of extra hours a day. They might charge like $200 per kid a month for this, or even more, and there generally isn't any oversight on the "program" because it's not actually being run by the school, and the nurses that work for the school aren't on contract to service this (hence the point about the medical liscences and so on), assuming this isn't all at the town green or a park, or some public blacktop or whatever.
The basic logic can apply to a lot of differant things though, and it's ridiculous, but it is a touchy subject, and not one you can actually take a side on easily if you really think about what's involved.