I have no evidence as to whether there is any correlation between how fast a cyclist goes and their likelihood of a crash
Then here's a data point. I've been riding in London at various speeds for 10 years. I have fallen off twice. Once was a clipless moment. Once was going up a dropped kerb that wasn't dropped as much as I thought, in the wet, at a snail's pace. So both my crashes were at considerably less than 5mph.
Obligatory helmet statement - I wasn't wearing a helmet in either case, and amazingly my head didn't crack like an egg. Possibly didn't even hit the ground - it's rather narrower than my shoulders, perhaps. But it's noteworthy that this is exactly the type of accident a helmet is designed for - low speed fall onto hard surface.
Oh great, I've commented on the helmet thread. Kill me now.