I hope to give some light from the point of view of an airbus pilot( a320) also with B737 and MD80 experience.
First of all I must say that is very difficult to judge what happened from outside, there is a rush of adrenalin if some important alarm starts at the cockpit, it becomes worst if you are flying in the middle of the night and turbulence. Problems that would be solved or the solution evident seating at home in front of a computer, become suddenly a mistery or insolvable because you lost an stabilicer or any other physical problem to the plane( it has happened before).
The first obvious mistake is going through the thunderstorm in that lattitudes, I personally know the pilots who where flying in front of them and they took a 200miles reruting to avoid that particular thunderstorm ( as other trafics did).
Then the reaction to the lost of information : as has been said the proper way to react is using thrust power % and pitch positions, there are tables for different flight phases , they are located at the quick reference handbook, but they should be located at an sticker close to the instruments( for inmediate use as speed limits for flaps or landing gear). An automatic help for recovering such a problem would be greate but computers do fail regularly in comercial planes( if web servers that are seating in a room fail imagine something that is suffering high doses of vibration, dirt, humidity changes, temperature changes, you name it) and you there MUST be other options.
When flying that high you are at whats called coffin corner, that is you are so high that the wings will easily enter both high speed buffeting and low speed stall( both will produce a lost of altitude control, you fall but can do nothing to avoid it).
Also the engines don't have enougth thrust( as fighters do) to support the weight of the plane. So the maneuver they performed seemed to don't make sense at all, why would a pilot pull the stick to put the plane deeper in the cofin corner inside a thunderstorm?.
I think the cause is precisely training( and possibly other interface choices made by airbus helped too ), let me explain: there IS a maneuver inside thunderstorms wich is trained a lot AND will make the pilot PULL the sidestick and apply TOGA power, is called windshear( avoidment). Usually windshear is the wind state that you could find near a thunderstorm close to the airport. Is caused by the first descending burst( thunderstorm madurity) hitting the ground (please google it as it is easier to see a picture than explain it). The result is that the big wind speed changes( in seconds) may put the plane suddenly in a stall
situation. Because it happens when you have no altitude left to recover from a stall ( maybe less than 3000 feet or closer than ten miles to the airport), your only possibility is to apply TOGA power and sidestick FULL back( the protections are NOT lost and then the plane takes care of the stall, the pilot takes care of the ground). This maneuver is practiced yearly ( or almost) as one of the most important ones ( with engine fail, traffic avoiding, depresurization), so it is my opinion ( I must say is not shared by many other pilots, many of them say it was the plane or simply don't know) and the simplest cause, that they simply were trying to fight a windshear, after all they were inside a thunderstorm and had to recover the control. That is way they simply couldn't understand ( or even hear the anouncement) why the plane was in stall, because they were folloing the procedure to the point. And procedures are to be followed if you do 't want problems with the plane and the judge( in a posterior investigation)
Also there are problems with the flight controls interface of airbus that have been known from the first a320 accident, and are highly polemic between pilots. Mainly airbus tried to reinvent the wheel at the cockpits,( and the rest of plane systems)in order to save weight. So they removed the link between the pilots controls ( except the rudder-fronwheel ones) and removed the possibility of the throttle levers to move acording to the power possition while in autopilot mode ( as boeing does ), after all only one pilot is taking the controls at a given time right?. But it is wrong, control feedback is fundamental in critical situations and has saved souls in the past. Also knowing the throttle possition at every moment just resting your hand at the levers while they move, gives you an amazing information of how the plane is behaving without having to look at the engine instruments ( there are one mm dots at the indicator showing the virtual "possition" of the levers, or where the thrust is going to move next), or simply overriding the autothrottle with out having to dissengage it. This throttle problem in particular has not caused a serious problem( that I am aware) yet, but give it time... Just imaging an autothrust setting the engines to iddle at 500' and the crew worried about having the runway insight in bad weather. The " don't make me think" principles still apply with airplanes ( and save lives, not only fuel) but airbus doesn't seem to bother too much.
I hope to have clarified a bit the problem from the Point of view of an airline pilot.
Pd. Sorry for all the misspellings, I am writting from my iphone. I'll edit at home.