Please help me!!! Do dentists usually provide a pre-certification?

I went to a dentist for the first time in the U.S. I got a dental insurance from my school (I got benefits by being a grad assistant for this spring semester) and I visited 3 times in May. I applied for the insurance in early spring but I waited to schedule an appointment until May because a lady at my school who takes care of insurance told me that there is 3-month waiting period and I can schedule an appointment anytime between May 1st and June 31. Now I'm in a big trouble because my insurance company said it actually effective on June 1st, not May 1st. I talked to the lady at my school and she said it is not her fault but the dentist fault because they didn't give me a pre-certification before even I made an appointment. Today I went to talk to the dentist and the receptionist told me that they usually don't provide a pre-certification for fillings unless the patient requested. We don't have a system like providing a pre-certification in my country Japan, and I didn't even know its existence. I don't know how to say something strong to protect myself in English. I don't know who's fault. I am just so afraid that I will end up paying more than $2,000 all by myself and I cannot afford it. Do dentists need to provide a pre-certification for a patient no matter what? Is there a rule or law like that? I cannot prove that the lady at my school said my insurance was effective on May 1st, although I wrote the date down right in front of her. In this kind of situation, what would you or people usually do in the U.S.? I need your opinions. Thank you.
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Dentists never do a pre authorization for the first appointment to do an exam and x-rays. They may, as a courtesy for the patient, file a pre authorization, once a treatment plan is made and a cost estimate is had. But they are not required by law to even do this. So your lady is 100% wrong when she told you that the should have filed a pre authorization before they even saw you for an exam, x-rays, medical and dental history, and the paper work to find out about your personal and insurance information.
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