AmEx Rental Car Claim – No Primary Insurance / No Police Report

I’m an F-1 student with no personal auto insurance. Rented a car from Hertz for 7 days, waived LDW, and paid fully with an AmEx Blue Cash card.

Accident happened due to icy/uneven road, car lost control and hit a log. No injuries or third-party damage. Authorities were contacted, but no police report was filed since none was required. Car was inoperable and towed to Las Vegas (~$1,300 towing).

Hertz estimate is about $12,500 for a 2025 Nissan Versa. I opened a claim with AmEx.

Questions:

1.  Can AmEx act as primary insurance since I have no auto insurance?

2.  Has AmEx rejected claims just because there was no police report?

3.  With this estimate, is the car likely totaled, and how much will AmEx cover?

Any similar experiences appreciated. Thanks.