ttown, think about it this way. Earth rotates - no doubt about it. Now imagine a geosynchronous satellite. It always hangs exactly over the same point on the Earth surface, so it always sees exactly the same view of the Earth - as if the Earth wasn't rotating. So, if you were living at geosynchronous satellite you would think Earth doesn't rotate, even if it does.
This is not much different from what happens to the Moon - it rotates, but from the point of view of someone living on the Earth it always shows the same side, so it looks like if didn't.