To the US insurer? Crazy as there is no coverage. How did they get the policy info?
Maybe I’m not understanding, if you rented from Avis then they just bill you for the amount of damage (plus loss of use , etc).
If you were in a collision and it was the other driver’s rental agency subrogating against you?
I’ll just say that I had two bullshit claims from Avis in Italy in '21/'22 that I had to block them from charging my Amex Plat.
Booked with Budget in Verona in '24 and my card was declined at the counter and I was really confused. Used another card.
Then I saw the declines on my Amex as something like: Avis Italy SPA. 
Didn’t realize the group ran everything as Avis.
I use sixt all the time in europe but i pay for the premium insurance. No hassle and everything is covered. Drop and run.