I know you're just elaborating the parent comment's point, so this isn't really directed at you, but the only study I've ever heard of which said anything like that was one academic riding a bike with and without a helmet, and measuring how close cars came to him. IIRC the difference was a matter of one or two centimetres and, perhaps unsurprisingly, the p-value was just under 0.05. That study was regularly thrown around by friends who were looking for a rationale for their dislike of wearing helmets.
We really need some high-quality studies with a much better experimental design that look at overall risk. Perhaps riders are marginally more likely to get into accidents if they wear a helmet, but I know from personal experience that when you do get into an accident you really want to be wearing a helmet - if I wasn't wearing one when I had a big accident about ten years ago, I'm pretty certain I'd have serious neurological problems now.
I linked to an article that I found on this in a sibling comment. It’s an average of 8.5cm closer when wearing a helmet. Obviously a p95 etc would be valuable here.
Personally, I believe the correct thing is to provide separate infrastructure from cars for bicyclists. One big nuance in the helmet debate is that the helmet is really best designed from mistakes while riding, ie when done for sport.
I agree. That same researcher has a lot of other research in the same vein. Having read some of the papers, I find them pretty unconvincing (and there are other papers which show that to the extent that 'risk compensation' is a thing, it's a short-term effect: if you increase the perceived risk of an activity, people may be more cautious for a bit, but they quickly relax into the same behaviour as before).
We really need some high-quality studies with a much better experimental design that look at overall risk. Perhaps riders are marginally more likely to get into accidents if they wear a helmet, but I know from personal experience that when you do get into an accident you really want to be wearing a helmet - if I wasn't wearing one when I had a big accident about ten years ago, I'm pretty certain I'd have serious neurological problems now.