The cable attachment point travels in an arc, and you don't need to double the radius to get double the circumference.

Yes you do.

circumference = 2 * (pi) * radius

therefore if you double the radius then you double the circumference

http://en.wikipedia.org/wiki/Pi
I wonder if it's that the effective pivot point is the center of the pin that holds the brakelever handle to the brakelever-handlebar mount... so if you measure the distance to the edge of the pin rather than the center of the pin, you will not get the effective radius.