What if you put the Batplane on a bat-treadmill?
brossa,
The problem I see with your argument is that you seem to be considering only the free spinning wheels and not the fact that the overall structure (the plane) has an engine pulling it forward regardless of what the wheels are or are not touching.
The wheels do not matter at all. The treadmill cannot keep the independently powered plane from moving forward, because the plane’s forward movement is in no way connected to what the wheels are doing.
To take off in that scenario, the pilot would have to be prepared.
VernWinterbottom, I suggest respectfully that you look at the link I provided on this. There are really really wise heads who are physicists who have looked into this. Your suppositions are not entirely accurate, depending upon the assumptions made about the situation. 
I was surprised that the pilot thought the plane wouldn’t take off. Don’t you have to have some idea how airplanes work in order to be a pilot?
I got a vague impression he was having fun and willing to play along.
The shortest way I’ve found to summing up why the plane moves forward while a car, for example, would not in the same scenario is as follows:
A car uses it’s engine to turn the wheels to push the treadmill to move forward.
A plane uses thrust from the engines to move forward. The wheels! They do nothing!
Try taxing without them, or without pontoons or skis.