In reply to GridNorth:
As Jim has pointed out, this is a legacy article, from before my time. As it is likely to cause more confusion than it is to provide good advice, I've pulled it from our website.
I worked for Lyon before moving to the BMC, and a method for paying out fast slack by briefly disengaging the cam was approved by Petzl for the original GriGri during that time. The important thing to note is that this method is explicitly different to that discussed in the article referenced above.
The thumb method is lethal because it involves holding the cam arm down in a squeeze grip, which when panicked you will naturally only squeeze more tightly. This disengages the cam, but to add to it, the thumb method also involves also letting go of the rope with the control hand. The end result is an uncontrolled plummet because the rope is not held by either the hand or the engaged cam.
The Petzl method for the original GriGri involves keeping the hands roughly in the usual belay position, and by rather awkwardly cupping the device prevent the cam arm rising with the little finger. This means that the rope is still held in the control hand, which is required to help initiate tension in the rope which then engages the cam. In addition, the awkward position of the hand means that a panic squeeze tends to slide the finger off the cam arm and allow it to engage - you certainly cannot apply as much force as you can with the thumb method.
The key point in Petzl's advice is to pay attention when belaying - when you do, you can anticipate the need for slack and hardly ever, if at all, need to use the fast slack method at all.
As it happens, I'm currently writing a 2 part article which explains how braking devices work, part 1 focusing on manual devices should be out soon.