As a parent, I can say that we do look out for other peoples kids. It becomes part your nature once you have your own child. I can't watch shows like Law and Order any more where kids are put in harms way.
The article states that the girl was in the hospital for 5 days? Knowing how hospitals work, the burns must have been severe. And, knowing how big cities work, replacing all those mats could be pricey. But Bloomberg is mayor who banned smoking in bars and restaurants. Maybe if this story gets some traction, the suit against the family will be dropped, and the city will do the right thing.
They should be publishing the name of the contractor or playground company in every article if they really want to get some movement.
The way this story is being framed, unless grandpa was boozing at the park or hitting on a jogger, then it looks like bully tactics and big PR problem.