It exactly matches the speed of the wheels. You may assume that it does this instantly and at all times. This is the key to the entire thing.
Most people don't get to that point because they are looking at the red herrings to do with unpowered wheels and airspeed. The mythbusters don't account for it, so that's why they're able to take off.
To have the instant speed matching operating at all times would take almost infinite amounts of power. Bad things happen when you have infinite power and instant feedback loops that are disturbed from equilibrium.
You end up with an infinite loop of accelerating the aircraft tyres with infinite power at any time the aircraft tries to accelerate by adding power to the system.