To get a perspective on how qualified, experienced pilots can make serious errors when faced with stalls and stick pushers, it might be useful to look over the Staines report. Also look over the report on the Airborne Express DC-8 at Narrows, Virginia. Both reports can be found on Embry Riddles' Hunt Library server at:
Online Full-Text Resources | Find Information | Alumni and Guests | Hunt Library | Embry-Riddle Aeronautical University
Follow the link to ASASA.
I was involved in the TWA 843 investigation, and it is correct to say that the airplane could have been flown. The first officer's AoA probe was defective, and actually had been for quite some time...that is another story. Nonetheless, all five (three plus two jumpseaters) pilots in the cockpit were strongly of the opinion that the airplane was not going to fly. That, plus the many thousands of feet of runway in front of him, led to the captain's decision to put the airplane back on the ground. There is no doubt in my mind that, if he had it to do over but had the knowledge we have today, he would have chosen differently.
I have always considered the cabin crew on that flight to be genuine heroes. I was in Paris when it happened; one of the flight attendants on my crew told me that I had better turn on CNN just before we left the hotel. I simply assumed, based on the images, that we had lost a lot of people and it would be a very stressful investigation. During the return flight, we did not know any more details. Following our arrival in Boston, I'll never forget going into the company ramp tower after we cleared customs. The veteran ops agent looked at us as we walked in, astutely read our faces, and the first words he spoke were, "Everybody got out. They're all okay."
292 people were on the pavement in just over two minutes, through two and a fraction of eight exits, without a fatality, despite a fuel-fed fire. Not a bad piece of work at all.