You are lucky, in most states you are guilty if you slam into the back of any car. That is from tailgating, if you were driving the safe distance, you would have had time to stop. The only exception here would be if you had stopped in time, but the person behind you slams into your car, and knocks you into the other car/cars. Then, that person who is last in line gets the bill for, up to four cars in front of him, up to twelve cars if the last person was in a mac-truck.
The legal distance in USA states is one car length per 10 MPH in ideal conditions, and twice that in hazardous conditions. (Snow/Rain/Ice) Up north, you also have to drive ten miles under the limit on rainy days, and twenty below the limit when there is snow on the ground.
If they established that you were not guilty, and the only question is that of money, then I would recommend getting at least three quotes, and take the highest quote to submit as your claim. Do not stand down... It costs what it costs! The purpose is to get your car back to the same condition as it was prior to the accident, this is also not only limited to paint and body, this also includes alignment, glass, safety checking of any air-bags and belts, frame alignment or shell alignment (For unibody constructed cars.), and personal medical expenses, including the appointment to see if there is any-thing wrong... even if nothing is wrong.
(Twisted frames/unibodys can be seen by looking at the door alignments and panel alignments. Doors or panels may be higher on one or both sides, not exactly matching the contour of the car. Unibodys are designed to fold in half to reduce injury, and low impact crashes slightly crush their folding points. Without proper reinforcement, this can cause injury in your next crash, or even cause you to crash. When the body gets a slight twist, a wheel alignment will limit vibration, but vibration may still be present.)
20Gal. Long (Green-House) and 55Gal. Tall (Primary Tank)
4 Fire-Belly Toads, 2 Fire-Belly Newts,
2 Giant Black Millipedes, 1 Grey Tiger Salamander