Well the media reports on this one are a bit of a giggle. The cover all of the go to words. Hero, plunged, terror, wrestled, nose-dived etc. The report is more sober, and much more interesting.
Basically this was an 'own goal'. The overall impression is of a crew who were uncoordinated, and not at all in charge of what was happening. Also worth noting that the captain only had 143 hours on type. I wonder what he flew beforehand.
When taking the aircraft off the autopilot, you should always press the disconnect button (twice). If it has disconnected by itself, then this will cancel the warning. The current AB will disconnect gracefully if you don't press the button, but you get the audio alarm. Boeing will fight you for control, but the control loading is so high that it's an instant reminder that you've not disconnected. I don't know how the SAAB behaves but some models are better than others....
This type of event has quite some history though. Whilst AB will disconnect, the 300 and 310 had a couple of quirks. They would only disconnect in the channel that had experienced an input (pull back, and pitch would disengage, but not roll) and they would not disconnect in the approach or go around modes. This variation of the rules, caused three major accidents that I can think of (two 300s, Taipei and Japan) and the Russian 310. Automation has many issues, but the interface between man and machine is one of the biggest problems. Inconsistent behaviour will catch people out.