Should the other driver caused my damage pay for the rental car insurance?

someone bumped the rear of vehicle, so his insurance is paynig for rental and body damage… in a meanwhile, im driving enterprise rental car. my geico insurance doesn't cover much right now, and enterprise rep asked i get their insurance and pay $19/day in case anything happens. i said ok… b/c it's an expensive new car.

do you think the other driver's insurance should pay this, or should it be out of my pocket?