Training versus the "right stuff"
@ Stud and 'bird:
I believe you can train folks to react to unexpected situations, although having a decent flying skills can be of great value. And you develop most of those via your training. I was given by a higher power decent "touch" or "feel" for flying, so basic maintaining altitude, heading and such wasn't a problem, and I could concentrate on making all the radio calls and clearing the airspace about me. But I know many great pilots that had to rely upon rote memory and standard procedures and having seen some unusual flight conditions during their training.
As 'bird has said, lottsa hangar flying and "what if's" in the flight shack can really help. In my case, I would sit in the barber chair or waiting room someplace and try to think of everything that could go wrong and develop my plan. Use the basic procedures but also think of cases where they would not completely correct the problem. My LEF emergency had no "procedures", so it came down to a decent FBW system and my own judgement whether to punch or stay with it as long as I had a semblance of control.
The military training exposes the newbies to many unusual attitudes and flight conditions that demonstrate that "there is a way". The war stories in the recreation bar also help, as in the case 'bird mentioned about the inadvertant gee-suit inflation or the pitot-static freezeup.
Serious training is essential to preparing the pilot for the known emergency conditions likely to be experienced and the unknown, but survivable ones. Helps to have some natural abilities such as being able to remain calm when everything is going to hell-in-a-handbasket, plus basic airmanship. But great training can supplement whatever natural abilities and such you already have.
That's the way i see it, but I didn't see it on AF447.