Not crazy. The moon orbits the earth in the same direction that the earth rotates, west to east. But the moon's velocity is 2288 mph* whereas the earth's surface moves about 1000 mph at the equator and slower at higher and lower latitudes. (Multiply by cosine of latitude.)
So the moon's shadow is moving west to east faster than the earth's surface.
Your explanation is correct. My comment was just a simple one because most everyone (I think) knows that celestial objects appear to travel east to west , at least here on earth. So if You posed this question to a 100 people I think most would assume an east to west shadow.