I am thinking back to basic schoolboy physics. Feel free to shoot me down in flames if I am talking B******ks, but I reckon its like this:
The load is effectively a pendulum. To become a danger to the tail rotor, the amplitude of the swing has to be a large angle (close to 90 deg). To initiate a swing, when you resolve the geometry, involves raising the height/ altitude of the load from its rest position = work/force required. The longer the line, the greater the distance you need to lift the load to get the same angle. So, the greater the force required.
So, when you have a shorter line, its more sensitive to sudden acceleration. A longer line will take much more acceleration to achieve the same angle of dangle.