I agree with Thomas' response that you are not doing anything incorrect. I work for an insurance company, and at point I was a member appeals specialist, and since the financial liability lies with the member, it is up to the member to appeal the benefit applied to these services with their insurance company.
It is fantastic that you are trying to advocate on behalf of your patients, however it is up to the patient to resolve this with the insurance company themselves. The patient's appeals rights should be listed on their EOB, and it is important that they review their appeal rights and the process, as they will have a limited amount of time to appeal the benefit, usually 180 days from the date of the EOB for a commercial insurance plan. If they miss the deadline, they will likely have no recourse for getting the claim adjusted to apply the correct copay.
You as the provider can certainly provide any documentation the patient might need to submit with their appeal but ultimately for commercial insurance plans your hands are tied in this situation.