Consider a coin which consists of a strip along one side made of a dense metal, and the remainder made of a light metal. This would move the center of rotation to the side of the coin. Now place the coin on your forefinger with heads up and the heavy band facing away from you. Assuming the rate of rotation was high relative to the falling rate of the coin, then it will tend to first impact the surface with the leading edge of the light two thirds, face down.

The article makes assumes that conservation of momentum guaranteeing a constant rotation rate guarantees fairness. But this relies on the assumption that biasing the coin cannot affect the timing of when it lands.

Of course, this doesn't bias the coin in either direction, it just lets the flipper choose which way to bias a particular flip.