If your child crashes his bike and gets a bloody knee on the playground, your relaxing afternoon at the park is most likely over and now you have a crying child, bloody clothes, a damaged bike wheel, and potentially another child who is now screaming because you have to leave the park to go find bandages. If your child breaks her arm, it's even worse -- off to the hospital you go, followed by a child who can't take a bath or get dressed by herself for a month.
Do some parents take this to an extreme and deny their kids some fun? Sure. But a lot of times, it's just about trying to maintain a level of mindfulness so that everyone can continue having fun for the afternoon.