Here is my theory: Random Events are not triggered randomly, but by the first person who does the action. This may appear to be random because there are so many people in a world at once. For instance The Mysterious Old Man would appear to someone who does an action, does whatever and disappears. Then he goes to another random person who does an action. This sequence may explain why it is rare see other people in the same place as you in random events (If you get teleported away). More Examples The tree imp will appear to someone chopping wood, and when it disappears (or is killed) harasses someone else.
The gravedigger appears to someone burying bones and once he is done, appears to another person. The Theory Part II Random Events cover a couple worlds. Thus, the frog prince(ss) might travel between world 1, 2, 3, or 4 at one time. That way it makes random events seem even more random!