That depends on the way it is linked. If it's linked causally in the opposite direction, your advice is quite dangerous. Meaning that if higher per capita head injuries are causing more helmet wearing in sub populations (maybe because they see more news about deadly injuries), than your advice is for people in those sub populations to not wear their helmets.
So it's relevant information, but the direct effect of "wearing a helmet cuts the risk of serious head injury by 60% and a deadly brain injury by 71%" is more important information.
You're right in the sense that if you die because your head cracked open like a watermelon on the pavement, that doesn't count as a head injury - it counts as a fatality.
Yes, note he stated "if head injuries are more common with helmets".
There have been some studies that correlate higher levels of head injuries with mandatory helmet laws. The thesis was that wearing a helmet induces more reckless cycling (higher speeds, etc) due to feeling safer. I don't remember seeing any good follow-ups studies either way and don't necessarily agree with the study.
The other theory is that helmet laws reduce casual cycling by adding an impediment to just hoping on and going. And that those short trips to the strore tend to be safer.
Personally my wife can't find a helmet that fits, Asians have rounder heads and north American helmet manufacturers are oblivious. As a result we never cycle.
That's possibly true. I wear a helmet when I go for a bike ride (for pleasure/fitness) but don't wear one when I run an errand by bike. The former, speeds avg 18mph, top out above 30mph, and use different roads. The latter, speeds are closer to 10mph and use mostly bike lanes and wide sidewalks.
So it's relevant information, but the direct effect of "wearing a helmet cuts the risk of serious head injury by 60% and a deadly brain injury by 71%" is more important information.