True. The OP's insurance company is likely to go after them for what the damage costs the insurance company. I hope you've already called your insurance agent as you don't want to miss any deadline for reporting the incident.

In some jurisdictions, it is automatically the driver's fault for hitting a parked car, rear ending another car, etc. Also in some states, you must report the incident to the police if you hit a parked car or if any auto damage exceeds a certain threshold. Your insurance company might need a copy of the police report or at least some number that permits them to retrieve the document.