I agree, a poll is in order.
The only way I can see how people are disagreeing on this is in the wording of the question. Here, as I understand it, are the two wordings. The first one is from the "plane won't take off" camp, second is the "plane will take off".
Wording #1: "The treadmill matches the speed of the wheels in the opposite direction" So using this phrasing, wheels @ 0mph, treadmill @ 0mph. If the wheels start to spin at 1mph then the treadmill would have to move in the reverse direction 1mph. Obviously in this scenario the plane would NOT be moving forward, otherwise the wheels would be spinning @ 2mph, then the treadmill would have to match 2mph and the wheels would go to 4mph, etc etc etc until everything explodes.
Wording #2: "The treadmill watches the speed of the plane in the opposite direction" Again, plane @ 0mph forward, treadmill @ 0mph, wheels spinning @ 0mph. Plane accelerates to 1mph, treadmill moves 1mph the opposite direction, and wheels spin at @ 2mph.
Now, I believe, there is a problem with the physics in the first one. But I haven't taken physics since high school, so I'll leave that to others more qualified to explain it, though it seems pretty obvious to me. But that's the only way I can figure people think the plane won't take off.