I keep hearing this, here and in other online spaces, but until I see link to one of these studies I'll be skeptical, because I don't see how you could test this in a meaningful way. I see very different people wearing helmets versus not. The people I see not wearing helmets tend to be taking leisurely rides around the neighborhood or screwing around on sidewalks downtown. The people I see wearing helmets are going longer distances and taking trips that span neighborhoods. All the delivery cyclists, racing/fitness enthusiasts, and commuters I see are wearing helmets. For myself, the risks I expose myself to are almost entirely determined by where I ride, which is determined by the purpose of my trip. Show me a study that somehow controls for that, and I'll take it seriously.
My personal feeling is that the "helmets don't help" line is a strategic choice made by bike activists who are doing work I approve of, but I don't trust them when it comes to my safety. They're fighting for separate infrastructure, which I like, but they're dedicated to the idea that the kind of riding I have to do to get anywhere is inherently unsafe. They aren't interested in making what I have to do now more safe; they're interested in making sure people in the future don't have to do it.