While it's a HIPAA violation, it is actually a mistake, and not intentioned on their part, sloppy yes, fineable not really.
HIPAA rules are very clear what is and isn't a breech of them, However .....To acutally make a claim that actions were intentional to break them is not often found.
You SHOULD speak to the Office Manager. Let them know you have someone elses bill and their account number. Shred it, let them reprint and send. The other thing is a lot of offices use an outside source to handle their billing, and billing issues, and if it's a major medical network, it is often done at a centralized location. The OM should be able to direct you though.
If you signed the form of financial responsibility, and your the last one to do so, you are on the hook for the bill. HOWEVER if anyone has signed one since, you are not responsible for the bill, at least in my state.
The financial responsibility form and the HIPAA forms should be different forms, and often will have different information on them. I would ask for copies of anything they are claiming your name is one. You have a right to those.
You may be able to barter the bill down as well, given their crappy response time, their mistake, and breech of HIPAA> They may just want to make it all go away if you raise a stink.