I have had significant issues with the hospital from my wife's breast cancer treatment that finally I had to escalate to the highest appeal level just short of filing a law suit. Thankfully we were successful.
I now use the following procedure when dealing with the insurance company customer service rep. First I require a full name and job title. If they won't give it I escalate immediately to the supervisor. Second, I ask if we are being recorded, which I know we are, but it reminds them of it. Third, I ask for the specific instructions as to how to get a copy of the recording. If the CSR can't or won't provide me the information, I immediately escalate to a supervisor. I take meticulous notes and request an email confirmation of the conversation. This way they can't spoof me or claim ignorance (incompetence) on follow up calls as this is in their conversation notes history that most companies retain. Every time I have done this, I have gotten results and accurate follow through.
Thankfully, our group insurance broker maintains a troubling person that is our advocate and she is very adept at cutting through the red-tape and BS. Still problems occur and we have to be diligent.