White helmets don't help AFTER the crash, they only help prevent multi-vehicle crashes. This is apparently due to increased visibility. 38% of motorcycle crashes are multi-vehicle crashes occuring at intersections. (Intersection being the junction of at least two roadways, or the junction of a roadway and a driveway)
A reduction of 63% in these type of crashes was observed in New Zealand, with similar results reported from a European study. This equates to an overall reduction in motorcycle fatalities of 24%.
The emerging theory of this measued phenomena is increased visibility. So far, I've not found anyone who has been able to construct an experiment, or a set of measurements, to prove or disprove this theory--and I have no idea how to do it myself.
An alternate theory has to do with driver's mis-perception of motorcyclists being bicyclists, and hence, traveling slower than they actually are traveling. This theory has also not been tested. A counter-point to this theory is the bicyclist crash data, for white vs non-white helmets. For bicyclists, it does not matter what color the helmet is. Also, bicyclists don't usually drive with headlights on in the daytme.
A third theory states that a motorcyclists head bobbles around as the motorcyclist is driving. This movement, that is of a bright white head, causes the human mind to perceive the oncomming motorcyclist. This theory has also not been tested. It seems more plausible than the bicyclist-based theory, though.
In short, we don't know why white helmeted riders have a 24% lower fatality rate. But we know they do have a significantly lower fatality rate.
We can describe why a lot of seemingly silly measurements reflect the real world. For example, did you know that kids with bigger feet consistently perform better on IQ tests? The reason is IQ tests are administered at usually only one time a school year, and all the kids are not the same age. But in the case of lower fatalities and white helmets, we don't know why. We only have theories.