Okay, let’s get this started properly. From the meat of the article
Helmet use is associated with odds reductions of 51% for head injury, 69%…
From the headline though (and repeated in the opening sentence)
Bicycle helmets reduce risk….
As a non-expert, who hasn’t read the study, that reads to me like a study finding a correlation and a journalist interpreting that as causation.
Random hypothesis: Helmet use is more prevalent among experienced cyclists, and they are more expert at dealing with crashes – inexperienced, helmetless cyclists more likely to impact hard and head first with the road / other vehicles, expert, helmeted cyclists roll, ninja-like and only catch the road with a glancing blow to the head.
No idea if the above is true, but it might be. The point is, that helmetless cyclists come off worse than helmeted ones does not, of itself, prove that it is the wearing of the helmet that causes the better outcome.
[retires to safe distance]