The Quick Peek is just one of those techniques.
When one is checking his own house for intruders, or even trying to negotiate in an outside urban environment, it quickly becomes apparent how many corners one has to deal with. And corners are dangerous places for the simple reason that they can have armed bad guys on the other side of them. Quick Peek enthusiasts suggest the armed citizen approach a corner and simply take a quick look around it. Just stick your head out, take a look and jerk it right back.
The obvious problem with that is that now the bad guy knows you are nearby. In fact, he now knows exactly where you are. If you come back around that corner to deal with the armed confrontation, he is ready for you. Also, if the corner in question happens to be sheetrock in your house, he may just begin shooting through the wall.
A much better tactic, if you know that you are dealing with a deadly threat, is to always let the muzzle of your gun go where your eyes go. With the gun at ready, you lean out to take a look. If there is an immediate threat there, you deal with it, immediately. There is no ducking back and forth to alert the criminal of your presence.
Of course, it is never a good idea to hug the wall, or corner. Bullets can ricochet down the wall and make a hit when, otherwise, they would have been a miss. It is a far better practice to get some distance from the corner before negotiating it. And, you should only expose enough of your body to take a look, usually just a portion of your head along with, of course, your gun muzzle.
I don't know where this Quick Peek business came from, but it is really a mistake. The defensive shooter should negotiate corners carefully and quietly. As you pop out for your look, have your gun ready so you can deal with the threat right then and there. Playing peek-a-boo with the bad guys is just not a good idea.