Let me say that I need an outside POV here because it's something I'm absolutely obsessive about and don't completely trust my own opinion. In my world, and it's not entirely solo, It would be commonplace to absolutely not say anything to others about something someone said to them, especially if asked to keep it private. If the players and staff felt anything close to the same, the only lack of communication would be with people outside the team. I expect by now that they have a clue who talks to who among the peripheral staff and such.