Good idea, Ron.
Yes, JMP should do better. I think what's going on is that there is an Overlay variable which is internally making N different point sets, one for each overlay level. Each point set is drawing its own selected points on top, but they don't communicate as well as they should.
That suggests another work-around is to use the Color role instead of the Overlay role. Color is only setting an attribute on each point rather than making separate point sets.