You are correct. Traditional X middle-button behavior is to insert the primary selection, from any application. It is distinct from the cilpboard(s), has no "copy" step, and doesn't behave the same as "paste" (it can't paste over another primary selection).
Many people don't notice the difference, though, especially if they're used to an environment that lacks that functionality, like Windows. Some might even get confused or frustrated when the middle click doesn't work quite as they expect (which, of course, is because it's actually doing something different).
@ericjmorey Oh you're right! Thanks for this clarification! π
Wow but that's an even better feature (didn't think that was possible) because for a lot of cases the clipboard is used for primary selections and then it isn't neccessary to take the detour via copy or cut (while you could go that way though) - that's fantastic! π