I don't know why airlines cannot just be honest with their passengers and provide accurate information particularly as regards rescheduled departure times.
If I know the inbound flight that I am subsequently travelling outbound on I will check the arrivals board (which is usually more accurate that the departures board) and see if the inbound is running to time.
Almost invariably if the inbound is showing as late the departures board will still be showing an on time departure - even at times when the inbound is going to arrive later than the scheduled departure time!