I've certainly never heard if that either, possibly at the time if the flight had already "departed" in the system then I could see an agent being locked out of it, maybe? Or maybe the agent you were dealing with at 4am in LAX had no idea or didn't want to mess with it. Who knows.

I had an instance last year on RDU-LAX, flight fully boarded, then cancelled due to MX, everyone off, rebooked to next day, I go home. Happen to check the app and see original flight now shows as delayed, not cancelled. I book it back to airport, run to gate, and get rebooked back on the original flight now departing in 20 mins.

In any event I would certainly HUCA this morning and/or go to LAX early and try several different agents (check-in, lounge, gate, etc) to get back on the original flight.