It doesn't matter what they are doing, it matters if the basis for claiming helmets are useful for cycling apply to walking. And they do. The testing bicycle helmets undergo is in fact approximating the speed of a walking person falling over on their head. Research has failed to support the idea that helmets offer a net benefit for cycling. I suspect the same would hold true of walking if people took the insanity to the next step and push helmets on walkers.

I imagine you catch your self more reliably when walking, too, and avoid head injuries.

Walkers hit their heads all the time. People die from it. And seat belts do not prevent brain injuries.