You are correct you most likely signed paperwork at the VW dealership making you liable for the loaner car when it was in your possession. Typically your auto insurance would follow you to this loaner car. If you had collision coverage on your car that was in for repairs it should cover the loaner car for damage to it caused by another vehicle or object (the ladder). If you do not have this coverage the dealership might be willing to use their insurance that was on the vehicle and then go after the at-fault person to be reimbursed.

If the insurance card, that the at-fault driver showed you, was expired I would still call the insurance company. Find out from them if the policy was expired or if the driver just did not have a current card in the vehicle. If the policy is still good put a claim in with the driver's insurance.