OK. I don't get it... It's pretty easy to see that the plane would fly regardless.

Whoever says that the plane WOULD NOT fly is thinking of a vehicles because the speed depends on how fast the tires can spin and the tires accelerate the vehicle by coming in contact with the ground.

This is not the case with the plane. It all depends on air speed.

Think about it this way:

You take a bottle rocket. Attach some wheels to it and let it ride on the treadmill. It's attached with a rope to an end of the treadmill so it wouldn't fall of. This way it keeps riding down the belt while it's steady in proportion to the surroundings. You lite that bottle rocket and what's gonna happen? I'll fly forward no matter how fast the treadmill spins.

The engines on the plane push off against the air and not against the ground. The tires are simply supporting the weight and reducing the rolling resistance.