I'm inclined to go along with hairy on this. It really doesn't take a rocket scientist to figure that if you take for instance a box lock with a short bar, as many of them have, having the same apparent balance as a side-lock with a long bar, also common, the balance point is "NOT" going to be at the same place in relation to the hinge pin.
The hinge pin's function is as a fulcrum for the bbls to pivot upon when opening & closing the gun & has little revelence to point of balance, just "Coincidently" happens to be "Nearby".

Miller/TN
I Didn't Say Everything I Said, Yogi Berra