From a fiddler's point of view: I can't look at my right hand, and they're correct in that if I look at my left hand I lose my place. (Maybe one reason I have so much trouble playing on Hearme is because I have to think so much about where my whole body is not to run into anything) I have had people tell me they are "amazed" that I can play in the dark.....? Fiddlers have to learn to play be feel.
From a "neophyte" mandolin player's point of view: If I trust my left hand, I am more likely to find the correct frets, but I HAVE to watch my right hand or I get the wrong string(s) or lose the strings altogether!
Mtn dulcimer: You bet I have to be able to see and look at the frets to be able to play. Tried to play in the dark once and embarrassed myself!
REF: Where do you look? Have you ever been to a concert where none of the musicians made eye contact with the audience? It's a creepy feeling. I prefer to make all the contact I can with an audience that has bothered to come hear me play, makes it more fun for everybody. I do agree tho, that sometimes you just have to shut your eyes to block out distractions, but I try not to do it too much or the audience will think I'm asleep.