Your response made me re-think my position as well. I read the statute you posted, and am now also wasting my daylight hours doing ScarleNation legal research, on exceptions to parental liability. Good use of my time, lol. I do agree that this apparently doesnt fall under parental liabiliity, because it wasn't a willful act - just an accident. I can't believe this woman called the cops for an accident involving a child.
So by the letter of the law, it looks to me like he can get out of it if he wants to. Not the end of the world, since the woman would presumably be able to look to the school for recovery. THat is who I really think is at fault anyway, since they need to not only control the kids, but also since it seems it is common for people to park in this area, and nothing is done about it.
Unfortunately, I think that also cuts against the kid, since it seems like "typical" included cars being parked in that location. If they generally allow that and do not enforce it, it is a gripe with the school/town, not with this woman. Maybe it is fair to offer the woman half, since both parties were in the wrong.
I am also surprised by the high glass deductible. I bet they are just too lazy to call the insurance company, because they want him to pay full price so they don't even need to do anything. Often, the deductible is much lower for broken glass. He could ask them to prove, in writing, that the deductible for broken glass is $1,000? Otherwise say he will pay half of the cost of the repair.