Though many people might insist that you turn your camera off, never stop rolling!
Controversial subjects are hard to get covered through video for obvious reasons. Documentary aims to get at the truth of a situation, expose what has occurred, and really understand the characters. For a number of reasons people may want you to end your filming even after you have begun, whether it is out in the field or in the studio doing the interview. No matter what you intend to do with the footage it is always better to have all the footage you possibly can than miss out on something because someone objected. This is why you must always keep the camera rolling, even when you are requested not to.
This is a common situation and your refusal to turn off your camera is not a moral concern one way or the other. If the footage does not serve the film and only exists to exploit certain parties then you will, or should, not include it in the film. If you end up having something important and ground breaking on your tape then it is your duty to use it as part of your project. You are the filmmaker and have the ultimate authority because it is your vision, but it is hard to tell in production if some of that footage is not going to be useful. That is why the post-production review process is the place to make those kinds of decisions.
This happens quite often in the field, especially when you surprise or follow someone that does not want to be on camera. They will often demand for you to shut your camera off, yet if you are in a public place the law is often on your side. No matter where you are it may enrage them to physical confrontation if you keep the camera on them. Try lowering the camera away from your face down to chest or abdomen level, but keep it going. Try to make it look as though you have turned it off but are still holding it in a fashion that will catch an image.
Though it happens more often in the field than it does in an arranged interview it still can happen. This is harder to distract the subject because the camera is remaining stationary and they have the ability to remove themselves from the lavaliere microphone. Just keep the camera rolling, and if you are on the camera you should walk away from it to pretend that you have finished. If you are conducting the interview you should try and distract them from the camera as much as possible and persuade them to continue.
Police, land owners, or other commercial and government officials may also demand you turn your camera off. Usually they will not have any legal authority to do so, especially if they are a government employee. Feel free to videotape police or other government people working in public areas, especially when it comes to their interaction with legal suspects. If you are on private property the rules are much different, but you cannot get in any more trouble for filming there than you can for just being there to begin with.
The two main things that will damage your illusion is the sound of the camera rolling and the power light in the front. Lighter cameras tend to make more sound, so if you have access to a larger and denser digital video camera you may want to go with that. The light can easily be covered by a tiny piece of black electrical tape. It is black so it will match black cameras, but if you have a lighter toned camera you may need to go with something else.
Stand Your Ground
The important thing is to keep going even though people are contesting. That is what separates guerilla documentary production from more mainstream filmmaking. You are there to film what others were too timid to do and therefore this is a risk you need to take.