squirrelking » first hit and I found this:
Well firstly http://www.helmets.org is (obviously) a helmet advocacy site, so you probably want a few pinches of salt to go with that. Though to their credit they do publish a reply from the original study author:
The full study had a lot of detail which obviously couldn't be included in a press release, and several other factors as well as helmets were considered. Your point about absolute distances is a good one, so you might be interested in one analysis in particular. I compared the group of overtakers who came closest with the group who left the most room, and you can see their data in Figure 2 in the attached document (you can also see exactly how close drivers came from Figure 1 too). What figure 2 shows is the ratio of particularly close overtakers to generous overtakers in each category - a score over 1 means there are more people passing close than leaving plenty of room. Note that the helmet effect varies with riding position, but leads to almost twice as many people getting particularly close in the 1.25m condition when the helmet was on, which is pretty interesting I think.
Even more interesting though is if you visit this publication of that study: http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0075424
and check out the comments, particularly this one: http://www.plosone.org/annotation/listThread.action?root=75587
which basically shoots down the re-interpretation and explains why incorrect statistical methods were used in it.
Interestingly if you check out the other published papers by those two authors they do seem awfully keen on helmet compulsion, with conclusions to their papers which ignore important and significant negative issues - I'm not entirely convinced they are totally unbiased.