OK, I'll play: no, they're not liars but they are mistaken. They are crashing, smashing a helmet and taking that as confirmation, which has various problems, not least that the helmet may have helped cause the impact (by some combination of the various possible methods already mentioned - this would explain why there is no significant population-level benefit) and that it's often difficult to tell if a smashed helmet compressed and absorbed energy before breaking up.
If you want a really vexing puzzle, try to find full crash test dummy tests of cycle helmets. The standard test is a disembodied head. The most I've seen publish is tests with a limbless torso. Why?
I looked because I was wondering whether a dummy with real flailing limbs launched from a bicycle (say a classic over-the-handlebars front-wheel-jam crash) is more likely to suffer a head impact if a helmet is strapped to the head, thereby slightly enlarging and weighting it. Isn't that a fairly obvious thing to wonder? Shouldn't the car industry test rigs be able to do this fairly easily? So why isn't anyone trying it? (Conspiracy theory: a motoring firm has done it and not published unhelpful-to-motoring results.)
The other thing I would note is that NZ is indeed a different road environment to the UK - it's far MORE dangerous, based on their road casualty statistics. So helmets should be more important there, not ineffective as it seems. (I have never visited Australia.)