So liability insurance - isn't that generally required by law in European countries? I know it's illegal to own a car w/o such insurance in Denmark, for instance.
Yes, everyone has personal insurance that covers your car for personal use. You can't register a car without that in all places I know of.
The issue is they also must have insurance that covers them for business use when they are using their car for business. Every personal insurance policy I've read says it isn't in effect when the car is being used for business purposes. If I tried to file a claim under my personal automobile policy it would go something like this
"...and you were driving for Uber at the time? Yeah...lol."