Since we're all sharing terrible insurance stories, I'll throw in my partner's. Of course this is not as bad as the OP, but it is still extremely frustrating.
We are graduate students and get a pretty good health insurance through our university's BCBS plan. She is financially independent from her parents, but she is additionally involuntarily insured on her father's EmblemHealth plan with no right to remove herself (her father could do this for her, but has refused to).
Last year she had some medical bills, and neither insurance company is willing to pay: the issue is that both plans have a clause that makes them secondary to any other insurance (this is apparently very common for student plans, and is also also somewhat common for additional family members on regular plans). For over a year now we have been sending certified mail to both insurers' coordination-of-benefits offices, but neither will acknowledge being the primary insurer and EmblemHealth has been ignoring us altogether for the last ~5 months.
The generally recommended strategy in this situation is apparently to involve regulators. However, regulation is state-by-state and and our university is in Massachusetts while her father lives in New York. Massachusetts' Division of Insurance found that the Massachusetts insurer (BCBS) was correct that the New York insurer (EmblemHealth) should be primary, but they have no jurisdiction to force the New York insurer to accept this finding.
The New York regulators were even more useless. New York's Department of Financial Services---the only state regulator for health insurance---responded that they had no jurisdiction to regulate the plan since it was self-funded (meaning that it is not technically insurance for regulatory purposes). The only remaining regulator was the US Department of Labor, but they eventually got back to us saying that they had no jurisdiction either: the problem is that my partner's father is a municipal employee of New York City, and for some complicated constitutional/political reasons the DoL isn't able to enforce labor laws on state/local governments.
I basically don't know what to do now. We have been on a waitlist for a legal clinic for about 4 months with no end in sight, and in the meantime regularly get mail from medical debt collectors. This is despite having insurance and making considerable effort to do everything "right." Clearly something here is extremely broken.