Your group insurance company has a right of subrogation. This term means that if another party, company, organization is responsible for the cost of your treatment, your group insurance company will want their money back.
Lawyers who have experience in handling automobile accidents can negotiate with the group insurance companies to take less money as reimbursement. There are a number of factors involved, such as how much money did you ultimately receive for your injuries from the at fault party and their insurance company. The lawyer can usually make a truthful and persuasive case for a decent reduction of the medical charges paid by your group insurance, especially if you were unable to receive in settlement sufficient funds to pay all your medical bills!