Could mandatory health insurance lower the cost of mandatory car insurance?

Does anyone else smell a legal zoo bigger than the mythological Ark
--------------------
Most health insurance companies do not pay medical bills if you are injured in an accident and there is applicable auto insurance that should cover the bills. Usually you see this with the ERISA plans (employer sponsor plans). Some private plans will step up and pay the bill....but ERISA plans usually don't. Even when the health insurance pays....they usually send a medical lien to the at fault drivers company. That means that the health insurance plan gets paid back for the money they paid out from the settlement proceeds. For the at fault drivers who would not have coverage under their liability coverage.....they have to use their health insurance. Auto insurance rates usually have to be approved by the insurance department of each state. These rates are pretty tightly regulated as it is. I don't see health care reform affecting auto insurance rates.
Source