Yes, it really is all about the pull

In lifting, there tends to be two mainstream schools of thought : (1) get under the bar as fast as you can and (2) pull as high as possible and go up on your toes.

Lets examine the physics of lifting. Your goal of a snatch or clean and jerk is to get the bar overhead. So is pulling really high or jumping under a bar relevant? How do we most effectively lift such huge weights overhead? Energy!

The bar must accelerate to the point that it travels upward. With weights that are a small percentage of your max, you are able to power snatch as the amount of energy that you would generte

Take Newton's Laws into consideration:
1. every action creates an equal and opposite reaction
2. an object already in motion tends to stay in motion

In other words, we can get that huge weight overhead by exerting a force against the floor of the platform to put the bar in motion. Ideally, as the bar is moving upward, we want to keep accelerating it until it rises above our head.

Now, we can easily accelerate light weights (70% or less of our max lift) overhead without going under the bar. That does change when your at heavier lifts. A lift close to your max will cause you to go under the bar as an assistance to catching the lift overhead.

You only need to go under the bar when the weight is too heavy to "power snatch" or "power clean".

Now, as smart weightlifters, we want to maximize the work that we put into each lift. With efficient technique, we can lift more for our given leg strength. To do this we must take advantage of the physics of our lifter-bar system.

You want the bar to accelerate in nearly a straight line, upward. After the bar hits its peak acceleration, it will begin to decelerate, eventually hitting zero velocity- it will be weightless. After the point of zero velocity, the velocity of the bar will change direction form upward to downward and continue to accelerate downward with gravity. The peak acceleration is where you exploit the hard work you have put into the pull.

You should be already moving under the bar before it begins to decellerate downward. You should not be fighting gravity to catch the bar. A perfectly timed lift will actually cause the bar to pull you out of the bottom postion, after the catch.

So where does this leave us with my first sentence: should we jump under the bar or pull as high as possible?
NEITHER! After your peak aceleration of the bar, you should follow through, naturally, with the motion of the bar. If you forcibly go up on your toes and strug, will tighten your arms and upper back, disrupting the kinetic chain of motion. Diving under the bar, on the otherhand, is a symptom of suboptimizing your pull. If you need to squeeze under the bar, then you have under acclerated the bar, and the bar is more apt to crush (not litteraly) you in the bottom position versus pull you out of the bottom position.

Those professing either (1) or (2) as the only way of lifting are really just describing two aspects of the lift, albeit, incorrectly.