I would assume they were talking about the stabilizer trim motor not being able to run the stabilizer trim because of the loads.
> When he pulled back, the elevator was ineffective; it didn’t do anything, so he said, “Well, I’ll use the stabilizer,” and the stabilizer wouldn’t run. It stalled, because of the load.
Key in there: "Wouldn't run."
Almost all transport class aircraft have the same sort of trim setup on the tail - they have the movable elevator at the trailing edge, and then the entire horizontal stabilizer can tilt up/down for trim. This is a lot lower drag than having the elevator deflected, and gives you an extra control surface for emergency use as well - usually, the control authority of the entire moving stabilizer is more than the control authority of the elevator, so you can use that in an emergency for pitch.
That the elevator wouldn't work effectively in the transsonic region was known - that's why they planned to use the whole moving stabilizer to pull out of the dive. Just, the air loads on it were too high with what limited authority the elevator still had, so they had to unload it again to run the trim, at which point they were able to recover.
The term "stalled" is overloaded an awful lot in aviation, but I'm pretty sure in this case, it didn't refer to an aerodynamic stall of the tailplane. There's virtually no way it could be aerodynamically stalled at ~Mach 1 without ripping pieces off.