What people (including pilots) do under stress is resort to simple actions drilled in by training. That's why emergency procedure training is a major part of pilot training curriculum.
What goes away first under stress is capability for complex reasoning, which is what one would need to figure out what the heck is going on and take appropriate action. In this case an a/c doing uncommanded dive can be a result of three things: elevator controls malfuncion (unlikely in modern jets, the mechanisms for transmitting control forces from the yoke to the elevator are multiply redundant and well-understood to be critical), structural breakdown (empennage falling off would do that), or run-away elevator or stabilizer trim.
In most a/c the runaway trim can be only caused by malfunctioning auto-pilot (that's why APs have multiple redundant ways to disable them), so the pilots faced this situation react by trying to disable AP in all available ways and then immediately jumping to conclusion that there's something catastrophically wrong with elevator system or even airframe integrity. The thought that there could be yet another system which can do major trim adjustment doesn't even enter their consciousness.
Training (and/or being in a position where there's no immediate stress of wrangling misbehaving a/c) would help to get to the correct solution (disabling trim motor by pulling the circuit breaker).
That said, flying an a/c seriously out of trim is hard, and can cause an accident on its own (the fine pitch control is gone, and you can even be so far out of trim that you cannot do landing flare no matter how hard you pull up, which in heavy jets would result in structural breakdown when the plane slams into runway).