When I was doing my experiment on born-contents, I discovered the zero-turn revolution too. When you have Pyramids, you can ask for a revolution at any time, save that turn, and when you come back you'll be asked which government you want, without changing turns. In fact, you could have 100 revolutions in a turn, if you thought it was fun.
I'd wondered before if Civ 1 had an equivalent to Civ 2's Oedo years. I just popped up an experiment and confirmed what Valen said: every 4 turns. You actually don't need a new government to switch to or even a city to see for yourself. Just push your settler around, revolt in 3940, and come back to Despotism in 3920.
Combining the two ideas, I tried revolting in a revolution year (like 3920 or 3840), saving, and reloading. It worked -- zero-turn revolution.
So apparently, the game has a concept of a "revolution turn," like an Oedo year in Civ 2, which happens every turn with Pyramids, every 4 turns without. Any time the game loads a revolution turn during anarchy, whether by starting a new turn or reloading a save, you get to switch governments.
Now Pyramids sound really stupid.