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Added a more appropriate reference (the previous reference actually partially refuted the claim)

Does wearing a bicycle helmet make the cyclist safer?

Does wearing a helmet while bicycling make an individual cyclist safer?

That is, in the case of an accident, is one safer wearing an helmet? If yes, are the odds of an accident lower, higher or identical if one is wearing a helmet? If the odds of an accident are higher when wearing an helmet, does the added safety of an helmet in the case of an accident makes the practice worthwhile?

To substantiate this claim being in the wild, here is The League of American Bicyclists' position on Helmet Use when Cycling:

Helmets are safety devices which prevent or mitigate head injuries in a crash or fall, not substitutes for education which is aimed at the prevention of crashes and falls.