Yep, it kills me that insurance companies (good ones, bad ones) all make you ask ask ask ask before they follow all of the rules. I pay for my own insurance since I have my own company, and I've chosen a slightly lower coverage rate just to avoid the big monthlies. But when I used to work for a different company, I had a maxed out plan, and they still would send me bills with balances owed by me, for every reason under the sun. I had to call, argue, dispute, and ask for a manager, the manager's manager, the manager's manager's grandpa, and only after repeated calls would they relent. When a family member had some bills for an emergency hospital stay (like, how many medical vendors get can provide help? Dozens!), I did all the calling, and it was amazing how much the insurance company pushed back on coverage. In the end, we got every nickel, but it took so much friggin' time.
That said, you might think I am for universal health care and am against private insurance. I'm not. I think universal coverage will be slower, harder, and more filled with unmotivated lunk-heads than private insurance. What private insurance needs is some penalties (enforced penalties) for setting up their workers to say No at every turn. The way to make money in insurance is to measure risks, know your population, charge the right premiums, and pay out when it's due; they should NOT make money by saying No and trying to skirt their own coverage policies.
Yeah maybe a little government oversight is needed there to police the insurance companies. But not a whole new government bureaucracy to run national health care! Yikes!
Anyway, I hope you are able to get them to pay up. Even if you left your last job before finishing the medical stuff, they should have offered you a continuation of your insurance, or if you're on a new job with insurance, that insurance company should be able to tell you who will pick up the bills. Good luck!
Manfred