The difference between fault and responsibilty is definitely something I plan to teach my kids from an early age.

If someone rear ends me when I'm driving safely and following all the rules of the road, it's not my fault. But it's still my responsibility to get insurance information, arrange for car repair and transportation, reschedule appointments, etc. I don't get to just walk away and hope everything takes care of itself.

It's just one of those unfortunate facts of life. Everyone has to handle things that aren't their fault sometimes.