> Now triple-click on one of the boxes - doesn't just that 1 box select for you so that you can move or rotate it separately from the other pieces? It seems to do that over here fine...

Yes Triple click is the normal way for select anything that have commun edges
(so as you can see on the image there is a little problem in case of commun edges of 2 differents objects from Moi! )



> As all volumes from Moi arrive in one component

> It should just all be plain geometry, I don't think that there are any components defined at all.

You right when you make "Open" in Sketchup

I have forgetten to precise that they arrive in one component when you make "Import"!!! :)
It's the same with import a true skp file (saved from sketchup) :)

PS As I reed and answser post in oder, maybe I made a redondant double answer :)