The three clue rule is simply about addressing the problem of the players not being able to go in any direction because they don't have information about the mystery in question. I don't think it is about keeping it moving towards a specific goal or path. It is just about it not grinding to a halt.
I was going to post the same things as what @hawkeyefan has posted here.If something is not moving toward a specific goal, then I don't know why we'd worry about things grinding to a halt. All of this is assuming that the players want to solve the mystery, or that the characters need to, for some reason in the fiction. That solving the mystery is the goal of play (however temporary a goal it may be).
The premise of the "three clue rule" is that the players need (in some sense of that word) to acquire the information toward which the clues point.