Apparently the entire issue came down to a junior pilot pulling back on the control stick, causing the airplane to stall and fall. It seems commercial airlines usually operate in a mode where it is impossible to stall -- pulling back all the way just ascends as fast as the plane can. But, the plane reverted to another mode of operation and the pilot did not understand this. Additionally, the Airbus control system has no physical feedback between the two pilot inputs and just merges the data. So if one pilot is pulling back, the other has no way of knowing. From the transcription, it seems that the pilots were confused as to why they were falling, until they realised the junior pilot was stalling the plane, and by then it was too late to fix.
Thanks for that description. Amazing that Airbus hadn't addressed this already. I've read that the initial problem that confused the pilots was the lack of air speed (and maybe altitude) data, due to frozen pitons. So I still wonder why the planes couldn't use GPS for that, at least as backup.