They didn’t push any extra insurance at all, but for peace of mind I still asked about it at the counter and ended up taking their full coverage for about €300. Not sure if it’s because I bought the insurance, but they “upgraded” my car (though personally I felt it was actually a downgrade). When I returned the car, the highway to Milan was jammed and I ended up more than an hour late. They didn’t charge any extra fees, didn’t even inspect the car – I just handed over the keys and that was it. (Maybe that was also covered by the insurance.)