I suspect that "Air Boss" in the civil airshow context, may be filled by an informed, but not necessarily licensed [for the role] person. Perhaps the chosen Air Boss is a licensed pilot, and/or air traffic controller, but I'm not aware that the role requires a dedicated license. As such, a licensed pilot, unless instructed by a licensed air traffic controller, holds the ultimate responsibility to maneuver the airplane safely, and avoid traffic. I opine that if not before, certainly now, wise people will think twice about taking on the apparent responsibility of being an Air Boss at an airshow with multiple airplanes in merging formations.
At a fly in at an uncontrolled airport decades back, for which I held an authorized role, an eager "retired air traffic controller" was enlisted to talk on the radio to air traffic. As he held no formal role, what he was broadcasting, was at best advisory, but more to the point, tying up the frequency so much that pilots could not make the broadcasts that they should have been (and were responsible to make). Seeing impending difficulty, I asked the organized to have that fellow's role (and time on the radio) dramatically reduced. Things were much better after that.