It sounds, even before my editing, that you expect the "leaning back technique" to allow you to brake to the point of skidding. That's not what it's for, and in fact it will prevent that sort of thing, to some extent. Plus it isn't "leaning" per se.

In any emergency stop on a bike, you need to get off the saddle and shove your body as far back as the reach of your arms and legs will allow you. Imagine trying to move back far enough to clear the saddle and sit on the rear wheel. That's the posture you want to adopt. The purpose is to counteract the physics of stopping, which by its nature transfers the majority of your weight to the front wheel. If you allow that to happen without tempering it a bit, two things happen - 1) the lack of weight over the rear wheel will cause it to skid prematurely, losing control of the rear of the bike; and 2) the weight transfer to the front makes it much more likely for the front wheel to lock up, and when that happens you will be going straight over the handlebars.

This very weight transfer to the front is what makes front brakes much more effective than rear brakes at stopping you in a hurry. But that efficiency in braking performace comes at a price - it's harder to temper the brake and control it so it doesn't lock up. Remember, when the front wheel stops rotating, it only does so relative to the rest of the bike (and you). Physics mandate that it continue to rotate relative to the ground. That means that the entire bike, and its rider, rotate about the axis of the front hub until you find yourself up close and personal with the pavement.