Well, you’re trained to push the nose down in a stall because stalls normally happen at a very high AoA, when there is not enough airflow over the wings, typically when you’re pointing up, not when you’re in a dive, and certainly not when you’re in a Mach 1.01 dive. And this was an elevator stall.

You’re not taught to pitch down when there is no elevator authority - in fact you wouldn’t be able to, by definition. But the problem here was too much airflow over the horizontal stabiliser - from what I can see, it hadn’t really stalled. Pitching down relieved the load and let them move the stabiliser. I suppose the combined deflection of the stabiliser and then the elevators was enough to get it under control again.

I for one am always pretty impressed with stories like these because they show just how well the pilots understand their aircraft.