PANIC is such an emotive word (esp to pilots) I would try to avoid using it!
Unfortunately many people think of 'panic' as hysteria.
Lesser symptoms of panic though are quite common....Im sure everyone here has seen another pilot (and some may admit to it themselves) just sit there stunned....and do nothing! The good news is that it is possible to come back from the brink of panic....often the other pilot starting a checklist is enough.
The 'fight or flight' argument is an interesting one in aviation. The problem arises from the fact that even having dealt with one critical situation pilots just cant sit back and say 'holy s1t, thank goodness thats over'....we still have the rest of the flight (and possibly other dramas) to negotiate. A fight or flight reaction tends to be instantaneous...an ETOPS emergency can take 3+hours.
Different training methods, SOPSs, checklists, memory items, 'immediate actions' (often verbal), and a reliance on facts, numbers and instruments are all tools we use to try and prevent panic.
I can tell you that after the shock of the critical situation...it oftens becomes almost 'routine' as you deal with it.
You mention GA. I have to agree that unlike the military or an airline they do not have complex training systems and testing/checking to reinforce these techniques but they do have a very good one...and one that I have heard from every pilot I have ever known. DO NOTHING! Sit on your hands for a couple of seconds.....put yourself in control and not the emergency.
1. Panic is an emotive and misunderstood word
2. Panic takes a myraid of forms
3. Many pilots dont know that their training systems are in part designed to prevent panic
4. GA do have organic systems in place....its just that often they are not explained to them correctly.