Note that I am NOT saying it is impossible to capture ANY water drop with only your shutter.
For example, using only your shutter, you very well might be able to freeze the motion of any of the following:
1) A water drop that has just left the faucet and only fallen half an inch. This would be moving at 0.5 mph, not 6mph, and thus could be captured without noticeable blur.
2) A water droplet that was sprayed into the air and is photographed at the top of its trajectory, where it is almost completely still. You might even be able to capture the motion of such a drop with as slow as a 1/500th of a second shutter, depending on circumstances.
3) A water droplet in freefall along with the camera (for instance, in space, or if the camera and droplet are both inside of a plane that is taking a nose dive)
4) A water droplet in a vacuum, where size is not determined by air resistance, and where a drop can be much larger and thus require less magnification.
5) A water drop that takes up a much smaller portion of your final print. For example, if the photo is a picture of children playing in a sprinkler, and the droplet only takes up 2 pixels, then its blur would only be 0.2 pixels of blur, which wont even be rendered. The fact that it is much smaller in the final print makes it easier to freeze its motion even at higher speeds.
6) A water drop that is so predictable that the camera can be made to pan downward (for example using a computerized stepper motor) and track its movement. This would reduce the relative movement from the point of view of the camera, effectively making the droplet act as if it were moving slower. With perfect tracking, you could potentially freeze motion with 1/50th of a second...
7) Who knows how many other situations?
But this is not about any of those. This is about the situation at hand: a drop of water that has fallen 1.5m (6mph), and is being magnified to take up 200 pixels in the final image.
I think what your arguing about is actually what you consider 'well enough to photograph it' was the point I was trying to make. Which I went on to say that I think you are trying to say there are better ways; ie closer to what you deem 'frozen'.
Frozen simply means "few enough PIXELS of motion blur (in the case of a quantum, digital image) in the final, distributed version of the image that the viewer cannot notice the blur."
For most people, this is going to end up being maybe 2-4 pixels of blur, tops, for it to be seen as frozen. That simply cannot be achieved for the given situation using shutter speed alone.