How responsible are parents for kids?

I was watching judge judy online and some kids did something stupid (drinking and vandalism). First, JJ ripped into the kids and REALLY ripped into the parents. I did stupid $h!t as a kid and was arrested for drinking at 17. I got a fine and community service. I told lies so i could go out and party. my parents trusted me and i betrayed that trust. But honestly, how responsible are parents for their kids doing stupid $h!t? I mean obviously they're responsible if the let it happen, but I'm talking about the kids who lie and sneak around to do it.