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Stats may be true (quick google throws up https://skeptics.stackexchange.com/questions/16027/are-you-more-likely-to-suffer-a-head-injury-walking-than-cycling which itself links to helpful UK road accident statistics) for killed while cycling, but injury stats (be it serious or not) seem to be far higher for cycling than for walking.
Also even if you're looking at death statistics, most of the people on this forum are probably traveling longer distances when cycling than when walking so if you adjust for time spent traveling maybe that changes - given that pedal deaths are 2.8/100m km and pedestrian deaths are 3/100m km, but I probably cycle 10 km for every km I walk, probably makes sense to take more precautions when cycling..
Do you wear a helmet when walking? The stats show that head injuries whilst walking are more prevalent (adjusted for distance) than cycling.
(I'm pro-choice, but just trying to understand the logic behind helmet use.)