Will it fly?

[Ginger]

Isn't the question whether the plane flies, given the treadmill motor can turn infinitely fast, thus making the runway move infinitely fast backwards, thus keeping the plane stationary, and on the ground.

That's only relevant as far as the frictional relationship between the plane's wheels body are concerned. A relationship which is negligable, at best. The plane will take off. The treadmill, realistically, can't turn fast enough for the Rex's angular momentum factor to matter.

In the case of the example, the fact that the treadmill is moving is irrelevant.