I think the trick in the question is that it leads us to assume that because the belt is running backwards that it prevents the plane from moving forwards. In reality it will only make the plane's wheels spin twice as fast.
If we had Chitty Chitty Bang Bang trying to take off under those conditions it would never move forward as its propulsion is via its wheels. I think that's the picture that we get with this puzzle - the belt preventing forward motion.
A plane, however, does not use its wheels for propulsion. It uses a jet or propellers to force air backwards (and itself forwards) and that force is not cancelled out by the conveyor belt.
An analogy is to have a rocket at one side of the runway which is fired forward. The belt will have no impact on the rocket as it's thrusting through the air above it.
Now, put the rocket on wheels (an ACME rocket :D) and fire it. It will thrust forward in exactly the same way as before and the only effect on the wheels is that they will spin faster than they would have done if the belt weren't moving.
I don't know if that helps visualise it better, but the plane will take off as it thrusts forward in the same way as a rocket, not a car. Trust me, I'm a smart arse.