As you will observe in the video provided, the barbed wire, when moved into the fence inventory, can end up being completely obstructed by static objects, making it impossible to be mounted onto the fence. Or they can clip into the ground depending on fence angle, making it very difficult to access them.

I suggest, to let it behave just as metal wire does when turning a fence into a gate. You can look anywhere at the fence with pliers in hand and the gate can be built. The barbed wire could function the same. Alternatively you could be required to look up for mounting the barbed wire when attached in the "up" and vice versa.