I would imagine that you would have to give all of your insurance info when returning the car, sign some documentation that you will submit the claim to your insurance co, and file the claim within a few days of returning home.
Try and use a Platinum card or other card that may offer you additional coverage if something happens. You may very well still have to file a claim with your insurance, but the card co may cover your deductible for example.
If you home insurance covers rental cars "loss of use" should be covered. However, having done this I have few suggestions on "loss of use". The company I used to work for would send a letter to the Rental car agency asking for "proof" of loss of use. Basically they wanted to know if ALL the other cars in the car class were rented for the period in question. Always worked, never paid "loss of use" LOL!
It's been quite a while since we've rented a car so don't know if things have changed, but when we declined the insurance we were told that if the car was damaged they would charge it to our credit card and we'd have to be reimbursed by our insurance co. They said they don't deal with insurance companies. Then they placed a hold on my credit card for something like $2,500.
I don't remember who we rented from. It was some cheap offsite company. Although we didn't have any problems, I won't be renting from one of those again!
cbrfan,
I kind of figured it was not one of the "majors" My brother had a huge fight with one of the cheap offsites a few years ago over insurance etc.... He learned. He is back to Hertz with me.