Under the circumstances you did the best thing. Most credit cards with LDW protection is "secondary" meaning you first have to file with your primary coverage with the company that covers you're personal auto first and what they don't cover, the cc will pick up.

However, there are a few cards out there ( Diners comes to mind) where the coverage is primary and you don't have to bother with your insurance company.

Consider yourself lucky. $60 is cheap for car damage these days.

However, I'm not one of those who generally thinks LDW from the rental companies is worth the money. It's typically a rip off. Most personal auto insurance covers damage to a rental car.