The thing is, if the airspeed needs to be 25kias, as in the show, obviously the aircraft will accelerate to 25kts by the force of the propeller, regardless of what is happening to the wheels.
Since the treadmill is moving the opposite direction at 25kts, the wheels on the aircraft must attain 50kts (in a no wind situation). The speed of the tires is really irrelavent unless in order to get to the required Vr, you exceed to the max tire speed, in which case the tires fail, the aircraft doesn't fly AND you have a real mess.
Sorry to keep this thread going...I was a naysayer myself, but in this scenario it makes sense. Of course, if the conveyer belt speed were to increase as the aircraft attempted to accelerate (tire speed + acceleration), then the aircraft would remain stationary, and there would be no relative wind over the wings.