If you push/pull a wagon, are you moving the wheels, or are the wheels reacting to your kinetic energy?

When you drive your rig, the engine turns the wheels directly (through the drivetrain) creating the forward motion of the truck. When you push a radio flyer, the wheels are reactive, not active. put a radio flyer on an old-fashioned treadmill (which requires you to push it to get it going). You can roll it right off and the treadmill won't turn, because you're not exerting any force on the surface.
The speed of the aircraft and the speed of the conveyor are independant quantities. The question does not say that the plane will be kept stationary by the conveyor, it says that the conveyor will spin at the same speed in the opposite direction. Ergo- plane travels 120 KIAS, conveyor goes 120 knots, wheels spin at 240knots until liftoff.

::eta:: Speed and force are different things. The conveyor can still match the plane's speed but not be able to push the plane back. It can't push the plane back because some clever monkey put wheels on the bottom, so when the conveyor pushes against the bottom of the tire, it just spins. Meanwhile the plane is pushing air and travelling at the same speed as the conveyor, but in the opposite direction. [notice I said "travelling", not "sitting"] No matter how much the conveyor pushes, all it affects are the wheels. It cannot push on the fuselage or any other part of the plane like the prop/jet can.