I was in an auto accident and now have medical bills. My health insurance paid them but doesn't the auto pay?

I have copies of explanation of benefits where my health insurance paid my medical bills from an auto accident. I live in the state of Missouri. Doesn't the auto insurance company still suppose to pay you the full amount of the bills?
--------------------
The health insurance company can "go after" your auto insurance company for reimbursement of any bills that they paid, if you purchased PIP or Medical payments coverage, up to your auto policy limit. YOU can't collect under both policies. Collecting under your HEALTH insurance automatically assigns them the right of "subrogation" - going after the other policy (either yours or the guy that caused the accident) for reimbursement.
Source