I know for a fact this is not true. I've had several flights that they actually did move the departure time much earlier than the delayed time. And people missed the flight. The last one occurred about 4 months ago out of SEA. I was shocked they would leave the pax since the gate agent said delay was at least three hours and they would call over the terminal PA and to listen up. Plane swap, and we left in 45 mins, and zone control said I had to go over my protests. With the memo that came out a few months ago that said flight operations controls if a plane gets to hold or not, that overrode me insisting on waiting on the pax that we were royally screwing over.