Your wrong in this argument simply because of the example I provided earlier with the die cast car and the sheet of paper. If you put a die cast car on top of a sheet of paper and pull the sheet of paper out from underneath the car, the car will not significantly move (it may move an inch or so, but it will not move the 3-5 feet that your arm moved). In this scenario, the sheet of paper can't overcome Newton's momentum law which states that all objects in motion tend to stay in motion (and all objects at rest tend to stay at rest). The exact same thing would happen to a plane on a treadmill. How is the treadmill supposed to counteract the thrust applied to the plane when it can't even counteract Newton's law stating that objects at rest tend to stay at rest?
Wait! I forgot!!! Your argument actually helps prove mine! All objects at rest tend to stay at rest. A plane on a teadmill is not in motion. Sure, the propeller is in motion, but the plane is not. Yes, the treadmill is in motion, but the plane is not. Okay, the wheels are in motion, but the plane is not. The plane is not in motion until it overcomes gravity and friction. Where in your argument is the plane overcoming these?