...make sure by checking your EOB that all their charges are your responsibility....
Yes yes a million times yes. Be sure to get on the phone to your insurance people with all your EOBs and bills (if any EOB has more than one provider on it, make a copy of that and circle the provider that matches a bill, on the other copy circle the other provider and match it up with its bill, etc), a new notebook and good pen, and talk with them to make SURE that you're being charged correctly by the providers.
Specific example of provider sneakiness: I once saw a general practicioner for general reasons, and she was contracted with my insurance company as a preferred provider. Which I knew meant she had to take what the insurance company gave her, plus my copay, and be happy with that and only that. She sent me a bill for what copay and insurance didn't pay. I immediately got on the phone to my insurance company, who put me on hold and immediately called the GP's office, and the bill was erased. HOW MANY people did she scam out of extra money in that way?
So make SURE.
What sort of provider is saying this about the 9 weeks? With a surgery, surely you're not getting just ONE bill. I'd expect a hospital bill, surgeon, possibly another one from the hospital for nursing care or assistants, a bill from the anesthesiologist, and maybe more. So there shouldn't be just ONE bill.
Break it all down, write it all down, get super-organized. If that's not your strong suit, or you're still recovering, get a close friend or relative that you think IS organized, and ask them to help. Not only do you want to make sure the billers have it right, you don't want to miss anything.
And when you DO make a payment, request a receipt, and put it in with the EOB and bill for that provider (I have notebooks and a 3 hole punch to keep this sort of thing organized, and once I have bill, EOB, and receipt together I staple them on an edge before putting them into the binder, to show that it's done).
Also know that many states (maybe all?) have laws about billing in a reasonable amount of time. At least in WA I think it's 6 months. DS was seen and had labwork done, and the bills came in, they were paid, and about 8 months later the lab sent something else through to insurance. INsurance denied it b/c it was too late, and told me that I was NOT responsible for it, because it had been billed too late. So make sure you don't fall prey to a provider billing too late, but acting like it's your responsibility, if your insurance company doesn't agree. They know the rules and must abide by them.