Is a provider allowed to bill above the amount listed on the EOB when they are in network on an HMO?

In 2020 I have some EOBs that state “paid according to provider agreement” that actually did not pay the provider anything for services and also clearly say that for deductible, copay, coinsurance, my responsibility is $0. The provider apparently tried appealing these claims, but the appeals either didn’t go through or the insurance didn’t get them. One insurance rep mentioned that it was because the provider didn’t include proper documentation. There are other claims that I did owe on and I paid the provider a lot of money already. But after learning from the insurance reps that I apparently do not owe anything on these claims, I’ve asked the provider to be reimbursed for the amount I overpaid, $1,500. But the provider says, “we don’t do that.”

Is this right? Are they allowed to bill me more than my responsibility on claims that say “paid according to provider agreement” on an HMO just because they weren’t reimbursed?

At one point I thought this is balance billing, because an insurance rep mentioned that it is, but now I’m not so sure. I read here that: “Balance billing refers to the practice of out-of-network providers billing patients for the difference between: (1) The provider’s billed charges; and (2) the amount collected from the plan or issuer plus the amount collected from the patient in the form of cost sharing (such as a copayment, coinsurance, or amounts paid toward a deductible).” So that doesn’t seem to apply because they are in network.