I am making a serious point about people having accidents, which you have avoided. Why do so many helmet wearers, you included, have these accident accounts? I don't think they are taking enough care, the care that prevents nearly all the non-helmet wearers from hurting themselves.
Cyclist death rates are quite low, and a high proportion of those killed are helmet wearers anyway, so large numbers of non helmet wearers just aren't having accidents of any seriousness. The only possible reason for that is they are taking more care.
.
OK, Tony, if that's the point you want addressed, let's do it on a proper statistical basis....
You make a claim and then propose an explanation. First of all you haven't established the claim - you haven't actually shown that non helmet wearers are having more or worse accidents. You have produced an anecdote that suggests that may be the case, but you haven't demonstrated it.
But let's move on. We need to decide what basis the statistics are on, eg., per rider, per journey, per mile. Suppose then that they do turn out to show that one group has a worse accident record than the other, it doesn't necessarily mean that there is cause and effect in one particular direction, or even that there is a correlation.
One classic problem in interpreting data is that there is some third factor, to which both effects are strongly correlated, and that is showing up as a weak correlation between the first two factors. To take a (probably untrue) example: helmets are a fashion statement for a certain age group; the same age group likes to ride wheelies along railway lines. The Daily Mail headline - scientists show that red helmets cause more brain injuries than green ones.
Another classic problem is that the methodology of the experiment is flawed. Here's another (and better) example. I sometimes wear one and sometimes I don't; I base the decision on the estimated risk of having an accident during the journey. Suppose Somerset is full of such rational people. Statistics will show that most riders having accidents are wearing helmets. Daily Mail headline: West Country yokels stupid; helmets cause accidents, when actually its the other way round. The accidents "cause" the helmets, and we're being smart.
My point is that there are correct and incorrect ways of working with statistics. If there is a positive correlation between helmets and accidents then that is an awful lot better than a negative correlation. (A negative correlation would mean lots of people having accidents while not wearing helmets.)
You raise a valid observation and I'm only objecting to your (mischievous?) conclusion. If there is a positive correlation between helmets and accidents then it doesn't mean that helmet wearing causes accidents, or that helmet wearers are more reckless. I've given one scenario where the correlation comes about simply because the riders are being sensible.
Nick