I would be careful with Private calendars.
I was released from the stake presidency, and I can still see events on the Church Calendar. Though they are shown as "Private Event," I can see the event details, including calendar name, room, and time.
Furthermore, when I sync my Church calendar with my Google Calendar, I can see all the meeting details, like any other event, including the Event Name.
This was not our intention when we set up that particular private calendar and was honestly a little disheartening to find that all the events over the last (who knows how many years) that we thought were private, actually were not.."