Insurance law varies from state to state and policies have widely varying language. What your insurance company is bound to [as it refers to their obligations to you to cover charges] is the language in their contract. Without providing a lot more information, all you can get here is some very general information that may or may not apply.
There are also contracts however between a medical [provider] and the insurance [company]. In order to get "in-network" status, most contracts agree that the provider will accept whatever the company pays for a covered procedure. The provider is obligated to accept this amount and does this so that they will get the referral business from the company. The company wants this because it makes their policy of value because of certainty.
This provision only applies to covered procedures however. If a procedure is NOT covered, then the contract between the provider and the insurance company is likely irrelevant where you are concerned and you are obligated for the entire amount [subject to reasonableness]. The company is not responsible to pay a bill because your provider says so.
This can put patients in a really tough position, and for this reason, many providers will have someone on staff who gets a procedure approved by the company prior to it being done. If that approval is obtained from the company, then the company is obligated to cover it as a procedure. This however, is most usually done by medical doctor's offices, clinics and hospitals as a courtesy to you and to ensure they will be paid, and probably less done by dentists offices. Ultimately, the responsibility to make sure it is approved is on you, not the provider unless the provider's policies flatly say they take responsibility for it.
Very likely, you owe this and don't have much recourse. Call it a life's lesson. There may be a justifiable reliance exception to all this however. If the dentist actually told you that they got it approved or that it was a cost covered by your insurance, then they induced you to do business with them because of a reasonable and justifiable reliance on their statements and experience.
A further point on this is potentially worth noting, and this is a matter of process, not law. The relationship between the provider and company is a tricky one that is not written in stone, yet is covered by very specific medical codes that relate to the health issue or medical complaint. In many cases, it is simply a matter of the provider adjusting the insurance claim submission to make the procedure align with the complaint... in other words, it's miscoded and therefore won't pass through the company's system. Second, I've seen cases where the provider called the company and gave the insurance company's doctor the rationale for doing the procedure. If that doc deems it reasonable, it could get waived through.
A final practical note is to beware of providers who sell you on procedures. Even a covered procedure may not be covered if it isn't prescribed for a specific complaint that you came in with such as pain or irritation. A doctor hearing a sound isn't YOUR complaint. It's his idea. As a side note, I have an ethical issue with doctors who volunteer procedures that aren't medically necessary because it is there merely to bump their profits. Often the patient gets stuck with it as you have. If they are going to do this, I think they have an ethical obligation to inform the patient that they should seek advanced approval from the insurance company before going forward.