I know that light travels in a more or less straight line through space from the sun to the moon, though. The only side that will be illuminated is the one facing the sun. That's irrespective of perspective, too.

When you talk about the path that the moon traces, are you talking about its daily path, or its monthly path? It would seem you meant the latter, right?

I just looked at Jeff Root's diagram too, and I don't like it either. The top half says it shows what your eyes see--but the text seems to indicate that the observer is under the moon, rather than away from it. I don't think you can explain this one with diagrams--it's just an illusion, it's not a real effect, just like the moon illusion.