Just a comment about the medical insurance part of it - Our insurance works this way (yours may be different) -
When a claim is filed, there is a place where the physician's office checks if it is work related or not and if it is due to an accident or illness. When a claim is due to an accident, before the insurance ever pays anything, they send a letter to the insured person to have them fill our the accident details. In this letter it states that if you get compensation for the injury from a third party, then the insurance company gets reimbursed. (Not the exact words, but something like that).
So, did you insurance company send you anything in the mail to ask the accident details?