Maybe you should have read the paragraph and not just the title
One problem is that people are assuming that ground speed and air speed are one and the same, when in fact they are not.

Take my Kites, for example, which fly based on the same principles as an airplane - only they have no groundspeed...which means they rely on the air moving past the kite to generate lift.

Again, it makes no difference whether the object moves through a static fluid, or the fluid moves past a static solid object. In either case, lift is acheived.

Taht's the other problem, people are assuming that lift only occurs if the plane is moving in relation to the ground, as they assume the ground and air move together - which is compltely false.

If I run 5 mph towards the east on a calm, windless day, I will feel a 5 mph breeze coming from the west - the difference between my velocity (5mph east) and the airs velocity (omph).
That is my groundspeed is 5mph, my windspeed is 5mph.

If I run 5mph towards the east with a tailwind at 5mph, I will feel no wind - because now there is no difference between my velocity (5mph east) and the airs velocity (5 mph east)
that is my groundspeed is 5mph, but my windspeed is 0mph.

This is important, because as the NASA link states in the "no motion, no lift" paragraph
Taking the conveyor belt -
Remember you have to use vector addition, and everything has to equal out.
If the plane is moving at 100mph, the Belt is also moving at 100mph in the opposite direction (add them together, you get 0 mph)
A person (impartial observer) standing off of the belt sees the plane staying in a stationary spot, and feels no windspeed (0mph). They see a person on the belt moving with the belt (away from the plane) at a speed of 100mph.

The person on the belt sees the plane moving away at a rate of 200mph (the combined speeds of the person and plane), and feels a windspeed of 100mph (the difference between speed the person is travelling on the belt and the speed of the air (omph) felt by the observer). The person on the belt sees the observer moving away from them at a rate of 100 mph.
The plane sees the person on the belt moving away at 200mph. The plane sees the observer as not moving in relation to it. The Plane also feels a windspeed of 100mph.

Now the vector addition -
The plane is moving at 100mph in one direction, the belt/person at 100mph in the opposite direction - they cancel each other out (0mph total movement)
The observer and the person on the belt see each other moving away at 100 mph (in opposite directions) so that cancels each other out. (0 mph)
The person on the belt and the airplane see each other moving away at 200 mph in opposite directions, so that cancels each other out. (0mph)
The airplane and the observer do not see any change in distance between them - they cancel out (0mph)
The person on the belt feels a windspeed of 100mph (because they are moving in relation to the wind at 100mph)- since the observer feels no windspeed, the airplane must cancel the person on the belts windspeed of 100mph out by feeling a windspeed of 100mph in the opposite direction (which would be going from head to tail on the plane).