A good referee is structurally smarter than the players in the game. The ref is outside the action but close enough to it to observe infractions.
A good coach is structurally smarter than the player they're coaching. The coach is not inside the player's body, so they can see how unhelpful this motion or that response to a situation is and how it interferes with better performance.
A symphony conductor is structurally smarter than the first chair violinist -- or any other player. They can see and hear from a vantage point that is closer to the audience than any single player and can therefore... orchestrate... the orchestra better than any single player could.
When I was younger I hated this. I was pretty sure the structurally smarter were getting paid based on unfairness.
Now I understand that at least part of their pay is for having to deal with the kind of young person I was. :)
Outsiders can cultivate structural intelligence that benefits both them and the insiders they serve.