Most of the companies should have written policies for these sort of cases. Either your company should have the insurance or they should offer you the option of paying or denying  for the coverage for the time you use their car  so that if you pay for the coverage, you are insured and don't need to pay for damages and if you deny the coverage you should pay for the damages. (It's similar to the rental cars where the rental companies ask you whether to take the accept or deny the coverage)

Ask for the company's written policy. Also ask why they didn't let you know either you need to pay for the coverage for the time you use the car or you need to pay for the damages before they lent you the car since now they are saying you need to pay for the damages.

If it is couple of hundreds of dollars, might not be worth fighting in court. But if it is in thousands, take them to court.