I think I figured out whats bothering me about it. We need to figure out at what point in the rotation of the coin it can be determined to have changed to the next face. Is it when the coin is perfectly vertical? Maybe even a few degrees before because the rotational velocity will likely carry it over to the next face after making contact with your hand?

It seems that in any case the coin does spend more time statistically on the face that it was initially flipped from, but it's not exactly (num_rotations/2)+1