It looks as though the important bit here is "re-engaged". If they had immediately initiated a G/A when the autopilot was accidentally disengaged, they would have been in compliance with SOP and would, according to earlier posts, have avoided colliding with the ground.
The burning question is would any other competent pilot put in the same situation have reacted differently? If you knock the kettle switch off while reaching for the sugar, your human reaction is to instantly correct for the mistake and turn it back on pronto. In that split second, while thinking about the ATC message, the embarassment of knocking off the A/P, SOPs are probably just too far out of mental reach. If there were many seconds available to react a less human, more trained decision may have been made.
Maybe there should be an audiable alert in such a situation, stating clearly "Go Around", to remove/minimize any chances for human instincts to jump in?
I have no jet experience whatsoever, but from earlier posts by 737 drivers, it appears that the rapid nose pitch up would be expected on this palne when the autopilot disengaged. It seems that when the autopilot was re-engaged (which may have been immediately afterwards-in a split second) the autopilot overcorrected, and put the plane at an attitude where neither an on target landing nor a G/A was possible in the space remaining.