Been handling auto insurance claims for 19 years. Yes, your health insurance should be involved with your medical bills, but all plans are different. Keep in mind the reason you are required to carry auto insurance has nothing to do with your well being; it's being able to cover anyone else you injure in an accident and cover property damage you cause in an accident. If you are uninsured and are at fault in an accident, and in some states that can mean 1%, the damaged party will be able to come after you personally for repayment, as well as taking action with the DMV to suspend your license.