Just a bit of information that comes to mind after reading the latest set of posts:
Transport category aircraft do have a third attitude indicator to allow the flight crew to choose "best two out of three" on the theory that two of the three won't die at the same time.
Attitude indicating systems are not connected to the air data systems in any manner that should allow the air data system outputs to influence the attitude displays. Generally the attitude indicators link directly to the inertial platforms and any air data information in the attitude indicator system is normally only data passed to the indicator for display and cannot modify the basic attitude indication.
That being said, the Airbus series of aircraft do not have control cables where as a last resort the flight crew can ignore all system inputs and place the flight controls exactly where their trained instinct tells them to set the controls. What I mean byt that is while I am NOT a software expert, i believe in any fly by wire system somewhere, somehow an electronic circuit passes judgment on the pilot input and decides whether to allow, modify or deny that control movement.
So one possible scenario could be: probes ice over and air data inputs begin to change, causing flght control software to make decisions on what to believe and what not to believe, causing flight controls systems to accept/modify/deny pilot inputs based on the software laws.
Note that I am not speaking of the autopilot and autothrottle systems as those systems disengaged, presumably as intended by design when the inputs became unbelievable. I am speaking of the electronic systems that interpret the signals from the side yoke, rudder pedals and throttles to develop and send signals to the flight control actuators.
Note that I am neither involved in the investigation nor am I a trained investigator. Consequently feel free to take my input with a grain of salt, and you would not be out of line to tell me I am full of it if your knowledge of Airbus systems is greater than mine (which would not take much).
The biggest flaw in my scenario from the available data is that the recorded data shows the pilot flying deliberately applied nose up input, and there was no indication that what the pilot was commanding was refused or modified by the fly-by-wire system. I only present my scenario to note that (in my opinion) we have taken the flight crew too far out of the control loop and if I were a pilot I would feel much better if there were mechanical cables between my controls and the flight control surfaces. And I think that mindset is reflected in flight crews that don't seem to go back to basic stick and rudder with complex failures.
I would think that basic stick and rudder skills would dictate the Attitude + Power = Performance could have helped, but I don't know that flight crews today pay that much attention to it with all the eletronic systems doing the monitoring. Flight crews from olden days could normally recite "at this weight at this altitude I use this throttle setting and this attitude." In these new electronic aircraft I don't know if the flight crews do that nowadays.
Also keep in mind that I have hundreds of hours on the flight deck observing and interacting with flight crews, but that has not occurred for at least 15 years. Thus I have NO flight deck time on a fly by wire aircraft from which to draw conclusions. Just one more reason to write off my comments if they don't apply to today's flight deck environment. I confess I am rapidly reaching dinosaur status in aviation.

)