I don't think there is any reason to assume there are any coaching circles that the sitting AD at Tennessee doesn't have access to. We are talking about advice here, not getting so and so's phone number.
I would think any AD at a program would seek the professional advice of an executive in charge of evaluating and hiring/firing coaches and a personality who works with and gets info from coaches on a daily basis to better do their job. The fact that they also have an historical tie, and still support the University would make their opinion even more valuable to me, if for nothing else to bounce my thoughts off of, to get a different perspective.
This is what highly successful people do and typically have in common. Never hurts to self evaluate and network on decisions. Notice I said highly successful people? Perhaps this is a part of what explains our failures over the years?
And it's not about having access to, it's about perspective and angles. The more you get the clearer a picture you have of your candidates.