Is the law that different? I know that in Germany it's quite hard to demonstrate that you have claims against the parents if their child damages something. You basically have to demonstrate that the parents really screwed up. If not, you are on your own. In Germany parents are most definitly not responsible for everything their child does.
And I never said that children have or should have the same rights as grown-ups. The law should only reflect that parents do not violate the child's rights without it being necessary and justified. And it does in Germany. I don't know about the US.
(Just one example about parent's responsibilities I remember: If, say, nine year old children damage a parking car on their way home from the playground it's imposible to make them responsible but it's also practically imposible to make their parents responsible. Going alone to and from the playground is, as long as it's not too far from home, a normal activity for nine year olds, their parents did nothing wrong.)