It doesn't actually. At the single incident level you would have to repeat the incident again exactly the same except wearing a helmet. Who knows, the door edge might have dug into the helmet and wrenched your neck instead of the scalp wound you got. Without the control case (and not something that was vaguely similar but exactly the same) you can't say whether your injury, even though it might be a different type, would have been less, the same or more.
And then there is the problem that if you wore a helmet you would hit your head more often because you would need more clearance to avoid the garage door hitting your helmeted head and your natural instincts are conditioned around sufficient clearance for your unhelmeted head, not the bigger helmeted one. Over a period of time that larger number of hits might mean you have more injuries wearing a helmet when helmetless there would have been no incident at all. I have hit my helmeted head on door frames a number of times in moments of distraction due to my only just clearing them without one. It can be very painful, especially on the neck.
Although you are probably right, probably isn't proof.