Quoted:
Is it an obvious case of the other party being at fault?
This needs clarified first. If it's obvious and the other is not disputing that they are at fault, then it's probably not a big deal. They are just wanting to get a statement from you to make sure everyone's stories' jive. However, if there is any sort of bodily injury or any other losses associated besides damage to an automobile, don't talk.
Another issue is determining who you want to in charge of the repair of YOUR car. Parts useage can vary depending on the ins. carrier or body shop. If you put the claim your ins. you'll at least know your vehicle is being repaired in a manner consistant with how YOUR policy is written. When you do this your ins. company with pay it, then subrogate(charge/bill) the at fault company. This process can take up to 6 months depending on the red-tape, but once it's settled you'll receive a check to reimburse you for your deductable, and the claim comes of your record with your ins. carrier.