Well, first off the category of documentary is probably more diverse than narrative. There are so many ways of executing a documentary and, subsequently, so many arguments for what qualifies as documentary.
Cinema verite (sometimes called "direct cinema") is actually an approach that attempts to address what we're talking about in the conversation about Michael Moore. Basically, cinema verite tries to bring more honesty to documentary.
The Maysles brothers (
Salesman) and Frederick Wiseman (
Titicut Follies) are canonical examples of this approach. In essence, the filmmaker(s) roll their camera and capture what happens with as minimal intrusion as possible. Of course, the mere presence of a camera changes the way people behave. Wiseman's solution for this when he filmed
Titicut Follies in a mental hospital was to show up everyday with his camera for months until the patients and the staff grew used to his presence and started to behave as they would if he weren't there. The results are shocking. When I watched
Titicut Follies, the experience changed the way I think about film. I defy anybody to watch that documentary and not be completely blown away. It's rather hard to find, though. You're best shot is to search large metropolitan or university libraries.