Upvoted for including counter-evidence in your post and changing your mind.

I was about to comment that adjusting the body's natural response might be dangerous if you ever did - after all presumably this system evolved to face pop-evo-psych cliches like the savannah lion and perhaps fleeing irrationally without thinking is probably the best thing to do in most of these cases. However, modern dangerous are different. For example, if you have fallen off a plane, you are more likely to survive while drunk or attempting suicide because your muscles are more relaxed and you don't panic on the landing and adopt a bad position. The savannah didn't have armed non-Pascal mugger's (which the best way out is probably not to fight or flight but to give him what he wants, unless your life depends on it), the option of calling 911, or machines that could instantaneously kill you from far away if they hit you in the right place, so it might be worth training to avoid the fight-or-flight mechanism in accordance with this post, even if it reduces reaction time if (the probability of you encountering one)*(utility you get from living) > (the opportunity cost of performing such training)