here's a clearer analogy: with the lens wide open it's like illuminating a set wit ha relatively large softbox, the light wraps around the object (in this case the dust particle) When you stop the lens all the way down it's like switching to a small spotlight, so the edge of the object's shadow is more clearly defined.
Interestingly enough, when I was first starting to shoot digitally (back in September 2001 with a D1X), I was having a persistent dust spot problem but it was only with one lens, a 20mm f/2.8D AF-Nikkor. The spot was really obvious when the lens was stopped down. We couldn't find it on the sensor and then my assistant had the bright idea of looking through the lens with a magnifying glass. There was a really tiny little spec on the surface of an internal element. I bought a replacement lens the next day as we were in the middle of an assignment that was due at a publishers by the end of the week.
Later I went back and started to look at really big projections of slides I'd been shooting over the previous year with that lens; now that I was aware of what to look for I could see the spec in those images too. I suppose I'd either been unconsciously ignoring it or had just gotten accustomed to its presence.