My supervised diet was with a nutritionist, so I was covered for both. The first appointment that I had was one on one with a nutritionist, the other appointments were in a group class with a nutritionist. My surgeons office has the supervised diets pre-organized for us if we want to participate in the ones that they offer. I figured that was easiest They know what the insurance companies require for the most part.
I'm not sure where you are located, but one of the biggest things I've learned with Federal BCBS is that it matters who your plan administrator is. BCBS Federal is the over seer of the plan, but they contract out to the various BCBS administrators, and that is who actually takes care of the approval process. For example, here in the DC area, if you are in MD or DC your administrator is Care First I believe, but in Northern VA where I am, my administrator is Anthem.