1. Mythbusters experiment is shit.
2. That jet plane lifting by standing on, has thrusters below him like a Harrier perhaps ?
3. Plane can't fly without actual motion to make aerodynamics work.
Deal with it.
Rudimentary creatures of blood and flesh, you touch my mind, fumbling in ignorance, incapable of understanding. - Sovereign
Mythbusters get many things wrong, but this time they did really a poor job. That "conveyor belt" is a joke.
Now to the OP:
Planes of the type shown on the picture fly when a lift is created on their wings. That happens when air moves around the wings.
Air can move around the wings (the same aplies for any object) from two possible reasons. When there is a wind blowing (the air moves and encounters a wing) or when the plane is moving (the wings move through the air).
If you have airspeed of a 300km/h and you are flying against wind that goes 300km/h, your speed relative to the ground will be 0km/h, but you will still be able to maintain flight.
Mhmmm just like I said, it's not a car and forward momentum is caused by air movement not spinney wheel movement on ground. The only thing the belt achieves is making the planes wheels spin faster.
While you're all correct in that motion is needed to create lift you're all assuming the plane can't move forward at all when in fact it's the exact opposite the plane will move forward regardless of how fast the belt is moving because the lawls of phix sez so.
It is also what is know as a "thought experiment".
In the 'real world' it would be technically impossible to build a conveyor belt big enough to hold a Jet and capable of reaching a speed to equal the rotational speed of the jets wheels when it is approaching take off speed.
However, this is a THOUGHT EXPERIMENT, so it is a given that it is possible, otherwise it wouldn't even be worth the trouble of coming up with it in the first place.
Following the rules set out in the OP, the plane is unable to take off.