I'm having massive mental agony over comprehending this and I don't consider myself a stupid person (although nobody really does, true of not). :)
I guess I really need to spend more time on theory, and shut up until I've done more reading.
It just strikes me that everybody wants to know about their grandparents and great grandparents. To a greater or lesser extent one might want to know about the people and happenings along his line of descent. But I, for one, couldn't care less about my 4th or fifth cousin living in Treekill, Montana, UNLESS it helps me nail down ggp 19, which it seems like you're telling me it won't.
Also, some people seem to be saying that a match for a 5th cousin, along with possibly being a huge meaningless mistake, might also show up in, say, a fourth generation, while others seem to be saying I should look higher, not lower, in 6th and 7th generation to find something.
Do the other types of DNA yield actual matches?