The problem is worded perfectly adequately, if one assumes a frame of reference of a point which is static at v=0:
The problem states that the runway moves with the same speed as the plane - if the plane is stationary the runway is also stationary.
The problem DOES NOT state that the runway applies an equal opposing force to the plane as that exerted by the plane engines on the surrounding air.
In the absence of a paint program and the use of algebraic symbols I'm not gonna start drawing free body diagrams, scanning them in, and writing the force-balance equations, but the upshot is:
There is an imbalance of forces - the plane accelerates, the plane takes off.
Step-by-step:
1) The plane begins to move - let's assume it moves at v=30m/s
2) The ground moves in an opposite direction relative to the plane at v=-30m/s.
3) The wheels are free to rotate about their bearings.
4) The wheels rotate as if the plane were moving at 60m/s, ie the planes velocity relative to the moving runway.
5) The plane doesn't give a crap how fast either the ground is moving or the wheels are rotating (Neglecting friction at the bearings - which, because they are bearings is negligible) - the only thing which concerns the plane is its own velocity relative to the air around it which (in simplified terms) creates lift.
6) The only thing the motion of the ground will accomplish is making the wheels rotate faster, and the bearings produce twice as much heat as normal due to friction.
7) The plane will take off.
Phewww! 4 years of studying mechanical engineering, and it seems some of it sticks after all.
Any arguement and I get the algebra out......
