In principle the rental company would not care if the renter has insurance, and has no obligation to accept an insurance offer as full payment. However, I wonder if the rental companies are intentionally playing rough with the insurers who write credit card policies because it diminishes their ability to sell waivers?

What we're missing, for comparison purposes, is information about how our personal auto insurance companies would handle these claims. Do they cover administrative fees or lost revenue, do they require utilization logs and do the rental companies resist providing them? Do they negotiate the repair costs, and do the rental companies then come back to the renter?