Guys there's plenty of stories around this forum about some of the more 'senior' members' real life experiences. As for myself, I've never (well almost) got into a fight outside of work (Military Police); so if I've managed it, then I'm sure you can.
Don't look for it and it won't find you.
As an MP you will have the respect or fear of soldiers drunk or not, then there is your size which will also no doubt be a deterrent, and the confidence and training you get as an MP. a lot of us do not have those luxuries.
I do agree with what you say though, Ive had more fights than most have had hot dinners, in the long run it just made me a bullet magnet if you know what I mean.