I have NOT read the entire article (and I probably should before posting, but I don't have the time right now, so here goes anway...) BUT
I think the gist is that one is a bit less careful riding with a bike helmet, ever so subconciously so. Just enough to get the general helmeted populace into a wee bit more accidents than the no-helmet riders. Reasoning being...without a helmet, one may be more aware of the danger and more careful...since one knows one is not wearing a helmet. WITH a helmet, guard may be let down just a little bit...making the chance for an accident a bit higher.
Again, haven't yet read the actual studies, but I have heard folks discuss the reasoning behind the argument. I'm not agreeing or disagreeing, just putting the reasoning out there.
Rock climbing is different, of course..I'm just discussing bike riding.