Accepting your copay means nothing. Your copay is printed on your card, that's all they were going by. Verifying with the insurance company just means that they verified you were covered, not that they participate. Payment is never guaranteed until the bill is received and processed by the insurance company.
But it is not your fault that customer service has not been helping you, I will give you that. You have been trying to do everything right. UHC works for the Medicaid office in this case, so (again) that is why I suggested appealing to their bosses. The department of insurance may also be able to help. I don't understand what kind of insurance plan, even a Medicaid one, can't even tell you whether a doctor participates when you call. That's like, the most basic of basic information you can ask for.