I recently handled a nearly identical case as yours. You have several issues here.
First, you should file a claim for the medical bills with your insurance carrier immediately and also contact the medical center's billing department and inform them of their error. You must demand that they submit the bill and also that they notify the debt collector of their error. You should also review the paperwork you signed when you obtained the medical services to see what it says about who is responsible for the medical billing ultimately - the medical center's billing department should be able to provide you with that.
Second, the attempts to collect a debt are generally governed by the Washington and Federal Fair Debt Collections Practices Act. A state violation of the FDCPA is also a per se violation of the Consumer Protection Act. The FDCPA requires a debt collector to observe certain things. Accordingly, you need to write to the collection agency and formally dispute the bill. Thereafter, the collection agency is required to notify any persons, including credit bureaus, of that fact when communicating credit information regarding you. You also should demand that the hospital and the collection agency immediately validate the debt that it they are attempting to collect upon. I have found that medical centers and debt collectors are quite anxious to resolve matters once the CPA and FDCPA are mentioned.
I suggest you complain simultaneously to the Attorney General's Office on Consumer Fraud. They have an online complaint form.
Third, I would have an attorney write an Answer to the Summons and Complaint you have recieved. If you fail to respond, the plaintiff may recieve a default judgment, further complicating your situation.
Last, you question the matter of the way you were served the Summons. This too is a matter to discuss with an attorney.
Service of process must usually be made "to the defendant personally, or by leaving a copy of the summons at the house of his or her usual abode with some person of suitable age and discretion then resident therein". If the person who received the Summons & Complaint was not a resident of your usual abode, then you may be able to have the suit dismissed for failure of service of process. It would probably be better if you had an attorney working for you.
It appears as though the insurance should definitely pay the medical bills.
[In accordance with the community guidelines of Avvo, this is not "legal advice", nor does it form an attorney-client relationship.]