First, I recommend you double check your policy. It's highly unlikely you have a 0 deductible policy, based upon averages. It would help if you posted the contract with sensitive information redacted.
Be wary of willy-nilly recommendations on how to pursue this issue, and certainly be patient because law is slow, yet in this middle stage of the US republic, the judiciaries still function mostly accurately, so if you are indeed on the right side of the law, you will prevail. Think of it as a game, and you will be better emotionally equipped to tackle this problem.
There are very specific procedures on how to handle credit and credit reporting issues. If you deviate, you will lose.
Reread your policy and be sure that it covers this cost. Post it, redacted of course, and it can be better analyzed.
From there, you can plan your response. If the insurer is indeed liable, consult with a lawyer, but be sure it is one who has a good track record of achieving results. If the prospective demands you prepay, they are most likely a hack.
If you are liable, the preferred route is to demand a pay for delete, but this must be pursued delicately because it will encourage the creditor to sue; however, creditors rarely sue for such small sums, thus the legal costs will eclipse the collection, so in this case, you can be steely. Never forget that they are your enemy: all compliments, flatteries, and helps are lies.
If you are not liable, the procedure to maximize the result are very precise. I would recommend opening another question or linking to one that addresses this issue so that a superior answer can be provided.
This is war. Never feel ashamed for trying to maximize your value. Creditors, reporters, providers: they all have no inhibition to see you enslaved, literally.
The overriding concern is to pursue this properly according to law.