You (or your health insurance) are responsible for paying the provider (e.g. the ER or hospital). However, the drunk driver will likely have to reimburse you: if the driver and/or his insurer do not voluntarily pay these bills, you could sue and would have a good chance of winning. However, despite the drunk's obligation (because in driving drunk, he was at fault) to you, you still have the obigation to the health care provider, which is why you have to pay (or have your health insurance pay), then seek reimbursement--since you are the ones who received treatment, you are the ones who has to make sure the provider is paid.