I am trying to figure out the same thing. Per the Chase Sapphire rep, the insurance is primary & it will cover any damage to the rental car upto the cost of the car. However, what happens in case of damage to another vehicle, who is responsible for that? The rep clearly stated that Chase only covers the rental car.

Excided_confused, what you inquired is the liability question. Read your European rental offer terms. It includes liabilities. This is different from the U.S. rentals. For example, here is what Autoeurope says:

Basic Package Rate Includes:
Value Added Tax (VAT)
Liability Insurance
Fire Insurance
Unlimited Miles

"Liability Insurance for injuries or damages to persons or things outside the vehicle."

All cars in Europe must, by law, be insured for third-party cover. So the car you hire has that insurance already in place. You do not have to pay for damage to another vehicle, or injury of passengers in that vehicle. The extra insurance you buy, or use your credit card for is to cover damage to the hire car and theft of it, but not necessarily from it. It may or may not cover damages to passengers in the case of an accident. You need to read the small print for that.

AMEX covers loss of use, damage to vehicle, stolen vehicle and injury to occupants of rented vehicle but not liability for damage or injury to the other vehicle. Do you opt for liability on the rental agreement or use your own home-based liability coverage (assuming the company you use offers that). So complicated! Thanks