After all these years, I finally know that it's real and I finally know why it's so elusive.
The Apocalypse mission, in which all UFOs swarm into Mega-Primus and start tearing down the city, is triggered when you destroy the Control Chamber and cut off the stream of UFOs. It's the aliens' last act of spite.
The reason it's elusive is because usually you've wiped out the UFO fleet by then, leaving the aliens nothing to execute it with. It'll only occur if you start doing the Alien Dimension missions while there are still UFOs flying around to fight you.