If the speed is the same, and the places traveled are the same, and the likelihood of an accident is the same...
Can you imagine going to a car dealership, and coming across a car with 10x the stopping distance and a center of mass twice as high as a Civic and the salesman telling you "it's just as safe so long as you're traveling the same speed and same places"? Would you buy that claim for a second?
I've avoided numerous accidents by being able to stop quickly on my bike, or by making a sharp turn. This varies greatly just between different bicycles -- a mountain bike has much better stopping distance than a road bike. There's obviously also a big difference between a skateboard and a bicycle.
There's also, I think, a steeper learning curve between skateboard and bike, though that may be because learning to bike as a child is more common. There's at least a difference in skill levels. I mostly know the limits of my bike. (e.g., how hard can I turn without skidding out?) and while a skilled skateboarder may be on par with me on that, I'm not. I can bike tens of thousands of miles without falling. I'm nowhere near the skill level of being able to do that on a skateboard.
Being able to eject yourself is also valuable. I suspect a skateboarder would have better "eject and run" options than a cyclist, so that's a point in their favor. (I've had my back tire run over twice, and both times I was able to simply run forward over the handlebars, and my hands (and head) didn't touch the grounds, but it's not always going to be that easy.)
Skateboards are slower than bikes unless you're really pushing it or bombing down a hill. Skateboarding is a skill and you can do all sorts of maneuvers to stop quickly, such as a side stop.
I think the main reason why skateboards are worse injury wise is many of them try to do tricks constantly, while most bicyclists are not in that category. Also the small wheels are more sensitive to potholes.
> the main reason why skateboards are worse injury wise is many of them try to do tricks constantly
Surely it's simply because of scenarios like a small rock's ability to insta-stop your board, basically guaranteeing your injury. Pretty much every time I've ever been knocked off a skateboard during my commute would be something you wouldn't even think/care about if you were on a bike. Not even close. One is a bike, the other is a heavy, tall pole (you) on a low, rolling platform. One is far more precarious, like keeping a reverse pendulum balanced.
Hell, the most common injury I've seen on a skateboard is just someone stepping onto one, misplacing their center of mass, and the board just rocketing out from under them, and then bruising their tailbone/wrists. Even an inexperienced bicyclist doesn't have a fail case close to that.
Most people really can't run much over 7-10 mph. A bike and a skateboard both easily go faster than this. Eject and run is not really an option unless you want to face plant or do a skilled tuck and roll.
This gets more true the further you are from sprinting on a regular basis. And really unless you have practice you're not going to match speeds with the ground anyway
I have to keep my feet under me for a few dozen steps while I come to a stop. I might not be able to do that at 20 MPH, but I think I can at 12 MPH. I can at whatever speeds I was going when people ran over my back wheel. (Once was a parking lot, so I was probably going fairly slowly, but the other was biking downhill.)
Go to the gym, turn the treadmill up to full speed and jump onto it, and see how it goes. That'll be a good data based test. The mill will drop speed by about 30% and most mills don't go up super high. Take a face plant for science.
If you did then you're probbably faster than normal and better balance than normal. I'm pretty sure I'd pull a hammy immediately. My coworker immediately face planted and broke arm and collar bone.
I commute on a Boosted Board and after three summers of doing so, I'm a very confident rider of it. But I wouldn't ever dream of going without a helmet, even for short trips around the neighbourhood.
I rode a skateboard every day for 8 years, from high school through college and thought helmets where stupid. I got a Boosted board last year and after one ride bought my first helmet. Would never use it without one now.