Except it won't
It might prevent some injuries in the case of a low speed or stationary off, but if it's motor vehicles you're worried about a helmet probably won't help.
My problem is that years ago I had the pefect helmet-friendly off. Relatively low speed (one foot still strapped in afterwards), no other vehicle involved, knocked unconcious, buckets of blud. A hat may or may not have kept me concious - I suspect it would but I don't know - but I'm pretty certain it would have saved me from the abrasions. I have no idea how it happened, as I have no memory of it at all. The memory of the aftermath, however, is the main reason I wear a helmet. I'm pretty sure a helmet would have made it a lot less unpleasant - and it was
very unpleasant.
Now, being 6'3", I frequently hit my head on things. I've been hospitalised - stitches and concussion - twice by lintels. Just last week I hit my head on a low beam hard enough for my legs to give way momentarily and dump me on the floor. It happens. And yet I don't wear a going-though-doors helmet. Some may see this as a kind of logical inconsistency. Which it may well be. But as Walt Whitman wrote:
Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)
Which isn't to say that I disagree even slightly with Boardman. Or that I would advise others to wear one. It's up to them, that's just my story.