I think you explained it yourself, when you shake the fuel, water and meths, the water and meths form lots of smaller droplets and can pass through the injectors/carb without a problem. The idea is to make the water and meths mix and not cause the engine too much of a problem this happens when you drive the vehicle as the fuel sloshes around.
Not sure about diesel as most diesel injection systems have water separators anyway, especially trucks with large fuel tanks that are very prone to condensation when partially empty. Years ago when I was driving down to Saudi Arabia it became part of the daily check routine to drain the water separators on the diesel tanks once you got into regions with hot weather during the day and cool/cold at night.
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