Probably the best explanation to this question I've come across so far, is the broadest. Richard Leacock says:

'What am I looking for? I hope to be able to create sequences that when run together will present aspects of my perception of what took place in the presence of my camera. To capture spontaneity it must exist and everything you do is liable to destroy it - beware!'

I like this quote because it is so broad that it is open to any form of documentary, and it emphasises the disruptive nature of equipment and your own impact on the environment, and people you come into contact with.

While this quote doesn't directly respond to the question, What is documentary?, it lays itself open to the form's possibilities by boiling it down to something quite simple. It also supports the idea that documentary should strive for the appearance of film truth, verisimilitude, rather than become the filmmaker's own vision (in the way a scripted narrative might be carved out of actors, sets and other mise en scene). Of course, these are all just more choices.