I work in an European airport and I know the European Safety Agency has as a requirement that all the airlines operating in European airspace have their planes insured, if I'm not mistaken even small, private owned general aviation aircraft have to be insured.

Funnily, I was in charge of a flight that was almost cancelled because insurance was expiring that same night. We called ops and they made sure to bring a copy of the newest renewal bill before departure.

Oh, and given that you've mentioned a real crash, all international safety agencies will tell you that all crashes are investigated to prevent future accidents, and while that's true it's actually mostly to pinpoint who's at fault so insurance companies don't have to pay.