I hope to shed some light into the kinds of situations that lead to an accident of this nature.
The Pitot system compares the pressure coming into the tube due to forward motion to the static air pressure. If the Pitot freezes over or is otherwise blocked, the airspeed will not change unless the static pressure changes, usually due to a change in altitude.
A decrease in altitude will result in higher static pressure.
As the static pressure increases the indicated airspeed will go down. This leads to a perceived slow speed condition which can be very hard to interpret if the aircraft is in clouds. The attitude instrumentation may indicate a level flight, but the airspeed and stall warnings may not.
In the opposite scenario, the pitot is not blocked but the static ports are. as the plane descends the lower pressure on the static side will cause the airspeed instruments to indicate an ever-increasing airspeed. I am willing to speculate it was a failure on the static side.
In this scenario the auto throttles would disengage to prevent an overspeed. Check.
The stall warning system may be triggered by an AOA vane. as the pilot flying takes over, he lost airpeed indication, and then it came back. If the plane has descended with a blocked static system, the airspeed is rising rapidly towards the Maximum Mach Operating speed. He will cut throttle and raise the nose, even though his actions are causing stall warnings. Exceeding MMO is simply that dangerous, and it can lead to fixation.
I speculate that both pilots locked into the pegged airspeed indication and did not interpret the conditions properly.
In flight training with the old conventional systems, we learn to trust that a certain aircraft configuration (flaps, gear, spoilers, etc) and a certain power setting (RPM, Manifold pressure, etc) will result in level flight at a given airspeed. The only variables that will effect that are airframe ice or faulty power indications. It is the fallback method to cope with all the possible flight instrument failures. Set the engine(s) to this, you get this.