Soup from the carcass is delicious, but there isn't time to do that during the meal. Even with a pressure cooker it's going to take at least an hour. (And if several tables order the same dish, you're gonna have a bunch of pressure cookers in your kitchen.)
So... the idea is sound, but I'm doubtful that they actually do it the way they claim. Which would make sense with the "hero chicken" story they admit to.