To my knowledge, the purpose of the NLG's presence has NEVER been to observe or document illegal activities committed by demonstrators - for Christ's sake, there are usually hundreds of police, often along with a dozen or so agent-provocateurs ready to do that.
The NLG's presence at demonstrations is to observe the POLICE, who have absolutely no official oversight at such events. The reason? I've been to lots of demonstrations, and I've never seen police officers wrongfully (or rightfully, for that matter) getting the *&^% kicked out of them by demonstrators - however, the reverse of this happens all the time.