I volunteer as a governor on a school governing board. Lots of people, teams, tasks (current, deferred and over-arching), meetings, committees, sub-committees, etc.
Trello would be an excellent tool for managing all of these complex tasks, ensuring none get dropped, and providing visibility to all. However, we have a legally binging duty of confidentiality.
So: since there is no locally installable product, how private is private? Can Fog Creek peruse the data? Or is it perhaps encrypted?