I ride a bike in London, don't own a car and am in my 60s, to declare interest. I don't wear a helmet and am unwilling to do so.
The arguments that I citing in the heading are summarised here: http://en.wikipedia.org/wiki/The_Problem_of_Social_Cost that is, neither car nor bike is particularly 'wrong' about any of this. The best thing [that we don't really have in London] is safe bike lanes.
So you've made the assumption that the only way you can have a head injury from cycling is by being hit by a car, and have built an entire argument around this premise then, huh?
Please allow me to relate the following two stories of accidents I've been personally associated with, one where the cyclist was wearing a helmet, and one where they weren't, with differing outcomes, and both occurring on cycling trails completely away from any motorized vehicles:
Back in the late 80's/early 90's, my brother (then a teenager) was riding helmetless on a cycling path, doing a good clip downhill when the front forks on his bike, without warning, broke off completely. As you can imagine from the physics, he landed face first on the pavement. He broke his skull in numerous places, broke his nose, jaw, and numerous teeth, had hair and skin ripped from his scalp, and suffered from a major concussion. At the hospital, my parents were told to expect that he may not make it through the night. He spent over a month in hospital, with his jaw wired shut. My grandmother sat at his bedside every day feeding him pureed watermelon through a straw. And while he has made a full recovery, 20+ years later he a) still has no memory of the incident, b) has numerous dead teeth, and c) bears the scars.
Two years ago I had an accident while cycling to work on a paved commuter cycling trail (a "mature urban cycling system" as someone terms such trails below), when I lost traction on a wooden bridge that spans a creek at the bottom of a hill. After sliding for 10m or so, my front wheel hit the pavement on the other side of the bridge at an angle, and I wound up going down hard. I broke my collarbone, impinged my rotator cuff, bruised all the ribs on one side of my bode, along with associated scrapes and bruises. I suffered no head injuries (and was assessed in hospital for concussion), but the impact at 20+km/h broke the helmet in half. I required a few months of physiotherapy for the collarbone, shoulder, and neck issues, but my head was fortunately unaffected.
So if you think your skull is somehow invulnerable, and there is no possible mechanisms for accidents and skull injuries because there are no cars nearby, then you are a total idiot. Helmets are cheap and effective, and there is no reason why any rational person shouldn't consider them standard gear when cycling. They do save lives -- and more importantly, minimize suffering.
I wouldn't wish what my brother and parents went through on anyone, including you. So good luck on your continued tempting of fate. I hope none of your loved ones ever has to hear the words "we don't know if he'll make it through the night" after you go out for a quick cycling trip.