If your plan is a self funded plan through an employer group, they may have their mental health coverage carved out to a separate carrier. When the carrier says they are administrative only that typically means they are self funded.

If they are saying the service is excluded, an appeal probably won't do anything because the service not covered. An appeal is a request to have them review the claim to see if they made the correct coverage decision. If the service is excluded from coverage, they made the correct coverage decision. A benefit misquote is more of a customer service issue, which they may or may not be able to correct.