Did your daughter sign a contract with the dentist before she was treated? Did you? Doctors and dentists ordinarily require all patients to sign contacts stating that they'll be responisble for all charges, whether submitted to and covered by insurance or not, or for any difference in cost and coverage, if that's waived, as it wasn't here.
Doctors' and dentists' offices often agree to submit insurance claims for their patients as a courtesy, but the health provider is still going to to hold the patient responsible for the treatment they get.
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I agree with the prior answer. Also, any debts incurred by a person who is 18 or older belong to that person. Unfortunately, if the debt is valid (i.e. properly billed and your daughter agreed to pay the difference between the actual bill and what insurance paid), then your daughter is responsible for this debt.
One option for having this removed from your daughter's credit report is for your daughter to dispute this debt with the all 3 credit reporting agencies. She must do this in writing.