Sure but you have to normalize it somehow. Americans drive way more than they bike. I imagine if you calculated this per-time or per-distance, driving would still come out much safer for the brain than cycling without a helmet.
I don't remember the source, take that as you will. Cars go faster which means a higher risk of collisions (less time to react etc.), and also a higher risk of head injury per collision.
Did you hit your head though? Even "low" speed for a car can be 20mph; you can hit a stationary object and be thrown around pretty severely.
That said yeah if you're "wiping out" more than like once every few years you're doing something seriously wrong (or at least taking an unnecessary risk). I've only once had any kind of incident on my cycling commute.
The hardest I've wiped out on a bike was where a bike trail intersected a road. Everything was super wet and slick from rain. Despite bikes having right of way and my bright bike light being on, a truck with no headlights barreled across it without stopping.
Once I saw it, I had to slam on the brakes so hard my rear brake cable popped out of the handlebar, disabling the rear brake completely and I was putting full pressure on the front brake. I didn't have time to react and avoid going over the handlebars, and I hit my helmet on the pavement. (Thankfully, I did stop in time to avoid the truck hitting me).
Was I doing something seriously wrong? Yes -- I was riding a bike without a properly adjusted rear brake cable. However, this sort of mechanical issue (and any number of others) could happen to any riders who aren't much more hyper-diligent about maintenance than average.
Who knows if we'd even be having this conversation had I not been wearing a helmet that night.
From a public health perspective, evidence suggests making helmets mandatory is counter-productive, and so I don't support those laws. However, I still maintain that anyone who cycles without a helmet is fucking stupid.
Cycling in the rain is a risk. Cycling in the dark is a risk. Cycling across badly-designed intersections (and if it put you as a cyclist in the kind of danger it wouldn't have put a car in, it's a badly-designed intersection) is a risk. Being on the road without a helmet - indeed doing anything in your life without a helmet - is a risk. In all of these cases one weighs up the risk of doing it against the inconvenience of not doing it.
Maybe we're all "fucking stupid", but by the stats someone cycling without a helmet is less stupid than someone driving, at all. There's this weird, disproportionate cultural obsession with helmets for cyclists and cyclists only.
What is this based on? My own intuition is that the risk is many times higher on a bike.