What type of coin are we talking about?
A coin with rounded edges won't land on its edge 1 out of 6000 tosses. A coin with a flat edge that is thicker than either of its faces (or just thick in general; doesn't have to be thicker than the faces) will land on its edge a great deal more often.
Also, a coin with a heavier "tails" side will more often land on heads in a spin.
I guess I should read the paper. Maybe it clarifies.