From my point of view, you're mixing up the terms 'speed' and 'force' a bit too loosely. The speed of the treadmill doesn't 'act on' the aircraft - speeds don't act on anything. It isn't valid to say that, as the speeds are equal, the forces are equal.
I guess it all comes down to how each reader visualises the friction component. From my A-level maths and physics, I automatically discount friction when considering this sort of problem. In theory, you're 100% correct - if the aircraft's wheel bearings produced loads of friction, or if the brakes were dragging, then you could have a situation where all the thrust of the engines was required to overcome the drag of the brakes, just to hold the aricraft at zero airspeed. That's definitely an assumption too far, based on the question, though.