OK now you know this, you should also know that it isn't true. What this is, however, is a nice way to visualise flycasting. It gives you 'feel'. If this was actually all there was to flycasting then we would be able to stick the rod in the ground so that it was standing upright, and by pulling the line against the top of the rod until the rod bent to it's maximum, then releasing it, we would be able to make a long cast. Truth is that the tip of the line won't even reach the rod. Try it.
So leverage is also important. Indeed it is an interesting combination, for it is possible to cast with rods which don't bend (broomsticks, short pieces of timber and one or two brands of flyrods), but if you have tried this you will rapidly come to the conclusion that a rod which actually bends is a far better tool.
In flycasting we are using both leverage and the spring of the flyrod. Your average caster gets the leverage bit just fine, but loses it when it comes to unbending the rod.
Anyway the more abruptly we stop the rod, the faster the rod throws the line. Working on this stop is the first secret to good fly casting. This part of the fly cast goes by many names: 'positive stop', 'forced stop', 'tip-snap', 'wrist flick', 'flick of the tip', 'flippetty flip', 'tip-top', and many others - but I'm sure you get the idea.
You know when its right purely by feel: you can actually feel the flyrod unloading at the end of the stop. You should be getting this feeling on both backcasts and forward casts, and every single time you stop the rod. This is the fly casting feeling. Some casters (possibly the majority) go through their whole lives never experiencing this feeling. Isn't that sad? Working on the stop is the quickest way to achieve results: especially a firm stop in the backcast. Often a great way to learn distance casting is to concentrate on a hard stop on the backcast. Just one of many strange paradoxes in life.
Learn this flycasting feeling by false casting a short length of line (perhaps 8 meters) using the minimum of hand movement. The movement should be slow, gentle and relaxed.

Do not fall into the trap of forgetting that the fly rod bends when we cast; therefore forget that rule that the line goes where the thumb goes - this is broomstick logic. When you bend the rod the tip comes closer to your thumb. This is not a matter of semantics, but is a basic principal behind flycasting.