I guess the fundamental issue is a difference in our interpretations of how the force works.
We agree that the forward thrust is created by the props acting on the air, completely independently of whatever the treadmill is doing.
Your argument is that the treadmill exerts an equal and opposite force on the plane than the props do, thus allowing no forward motion of the fuselage, therefore no airspeed, therefore no lift. This is where we disagree.
Consider a theoretical frictionless world where the treadmill is moving and the plane is not trying to accellerate; I believe the treadmill would simply spin the wheels and exert NO force in a rearward direction on the plane. The bearing in this situation is a frictionless lubricant separating the plane from the treadmill.
If I understand your position, you're saying that even in the frictionless world the treadmill would still exert a rearward force on the plane.
In the real world, the purpose of the bearings is to minimize the unavoidable friction as much as possible thereby allowing the fuselage to move back and forth on the tarmac as easily as possible. If the bearings were unable to reduce the force of the tarmac on the fuselage, then the thing might as well have fixed wheels. The plane would be unable to take off regardless of what the treadmill is doing unless it could generate enough force to overcome the static friction between the tire and treadmill.
So, my summary point is that the bearings serve to minimize force from the tarmac on the plane, therefor there is a net vector of force in the forward direction.