No, the insurance company is saying that they will not insure the tot lots at all if non licensed people start digging it up. So when a child falls off the slide and breaks their arm and someone wants to file a claim against the insurance company to cover medical bills or a child trips on a rock and falls and hits their face on something over there and needs stitches and mom and dad want to file a claim with the insurance company to cover medical bills, they won't cover it because non licensed folks messed around with tearing up the lot. They aren't saying they won't cover the few volunteers working there but that they won't cover the lots at all EVER for anyone because they were messed with by non licensed people who they (the insurance company) figure probably don't know what they're doing. Things have to be done to code blah blah blah for insurance companies to cover things. It has nothing to do with the property managers (other than looking into the policy), the insurance company will cease to insure any incident that happens on any of the tot lots ever again because they were messed with by non licensed "contractors".
That's the way I understood it anyway. Hope that helps to clarify it a bit (if I'm wrong someone plesae clarify)
I agree with Brad though, I'm sure someone in the community who is a licensed contractor wouldn't mind supervising so that it was "done" by a licensed contractor without the expense of a licensed contractor, GREAT idea IMO.