It seems like this is not yet settled. This meta-analysis of studies concerning increased risk-taking found that most studies with experimental data did not find that wearing a helmet increased risk-taking behavior. The author mentions the downhill biking experiment and suggests that there’s a distinction between taking more risks because you are wearing helmet and riding slower because you feel unsafe without one. This is supported by the habitual non-wearers not increasing their speed/risk when wearing a helmet.

This Other analysis looks at the actual rates of different kinds of injuries and finds that helmets significantly decrease the risk of head and face injuries while not having a significant impact on neck injuries.

This study of hospital stays related to bike accidents shows that hospital stays were significantly more frequent and severe for those who didn’t wear helmets. (and it examines some of the potential cultural hurdles in expanding helmet use).

Overall, I’m most influenced by the last study. Theoretical analysis of risk taking and injury type is certainly important, but the real life data in this and other studies indicates that wearing a helmet strongly correlates with a decreased risk of injury and death.