First, collect facts.
From the collector: You need to "collect" (heh) the account number, doctor or provider's name, service date, amount, and contact information for the doctor and the collection agent. Hopefully, it's all on the letter and you won't need to contact them to chase it.
From the doctor (the one telling you that you are paid in full) you need to collect account number, service dates, amounts that are paid/settled, and their contact info.
The purpose of this exercise is to establish that we are actually talking about the same bill. Because in USA medical it's very common to get simple care for one thing, only to find this accrued 2-3 bills from different providers of various sub-services.
If the bills match up
If the bills indeed do match up, i.e. Same doctor, same account number, same dates, then contact the doctor's billing offce and ask them to state in writing that your account is paid in full. They are going to have a HIPAA problem with that. That is 100% valid, and do respect it, as it protects you. However, that still allows sending the info by postal mail, or by you picking it up at their office. Be nice, but insist on this.
Once you have this "get out of jail free" card in your hands, now you can cheese them off. Now send them (again, postal mail or hand deliver) a copy of the collector letter with a cover letter giving a good tongue lashing... tell them to call off their dog. This should invoke a huge Whoopsydaisy!" from the doctor's billing office.
Another option is to refer the collector to your insurer. You should generally keep your insurer in the loop.
If the bills do not match up
Your next step is go talk to your doctor's billing office and ask if they know anything about it. It may be what I described earlier; a separate service provider fee.
Regardless, it's time to pull your insurance company into the loop. It's possible the insurer is supposed to pay this. They can certainly advise if it's valid and what your co-pay should be. Generally if the insurer tells you to pay it, pay it.
Or haggle it
If you reach an impasse where you can't avoid paying it, push back on the provider and offer a fraction, e.g. 1/2 or 1/3. From their perspective, the longer you take to pay, the more unlikely they are to collect a dime. So 1/3 starts looking good.
Further, the US health system is positively psychotic about how they bill. For instance, one dialysis treatment (you get 3 a week) bills out at $13,800. However Medicare only pays $400, and the dialysis centers cheerfully accept that and live off that, because private insurers pay about that too, and Medicare takes over all dialysis after 3 months.
The insurers strong-arm hospitals and doctors into accepting sensible rates ("Reasonable, usual & customary", RU&C, or R&C) for services, on condition of being "in network" - and they can't afford to be in nobody's network. There aren't enough cash-flush "retail patients" around.
So the medical system insanely overcharges "retail patients" -- on the idea the uninsured indigent won't pay regardless, and this lets them get max possible dollar from insanely rich foreign medical tourists. (Who come from poor countries with awful medical systems, think Kuwait).
The upshot is that medical collectors are very accustomed to getting shockingly lowball offers, because their retail rates are shockingly highball compared to "reasonable & customary" insurance rates... And the lowball offer may still be more than they get from insurance, so still a net win.
The "Reasonable & Customary" amounts, which you'd need to research, are a good place for an offer. I'm not advocating welshing out on bona-fide medical bills from good doctors, but rather to resolve a wrong amount in collections. Some might not like that, but the rest of us have limited time and must choose our fights carefully.
I make them sign an agreement that this is a bona-fide dispute over the validity of the bill; therefore nobody will disparage anyone else, including to credit bureaus; and no amount is being forgiven, so no 1099 should be issued.
Some people have a problem paying the "collections industry". However in medical, a bill uusually spends at least a year with the original creditor (i.e the doctor) before it is sold off to third party collectors. I am advocating settling up in that time, so the doctor or lab gets some amount resembling the R&C amount they get from insurance. Keep in mind in this time you may be dealing with a collection agent, but it is still a doctor-held debt and the doctor benefits from the settlement.