False analogy g00ner, a kitchen needs an incredible level of coordination between all the cooks and the server. The chef in a kitchen would be the equivalent of a player-coach in hockey.
Not false at all but you can sub in any hierarchical organization if you don't like basic service industry analogies.
Every team has levels of leadership and accountability. What's being said, in a contrarian vein most likely, is that the coach doesn't choke and it's on the players to produce. This is just not how the real world works. Accountability works upwards. That doesn't mean there's no accountability at the bottom, it means the greater and final responsibility rests with the person who is IN CHARGE. That is literally the definition of their job...to get results from their team and take responsibility for that mission.
Is gmbm the right guy? If not, replace him.
Is BT the right guy? If not, replace him.
Is player x the right guy? If not, replace him.
So start at the bottom. Has BT had a roster good enough to win the Cup? If "yes" then gmbm has shown he can do the job and your next glance is at BT. If no then that relieves some of the pressure on BT and some of the players. Get a better GM who will assemble the right team, then re-evaluate.
Has BT had the players to win the Cup in his time here, and in Nashville?