All of the above arguments obtain if the fluid is a closed system and is only acting as a result of the forces it itself is exerting upon itself, subject to the various boundary conditions around it.

Of course if you open the system various outcomes are possible depending on what the external influences do to it (for example, the two solutions mentioned for the still water become entirely plausible if there's somebody roaming around who might put a lighter under the glass and cause the water in it to boil, but that isn't the point of the exercise).