Through lift redistribution winglets probably have a very small increasing effect on wing root bending moment. That is not the point though. The fuselage section on top of the wing box is not going to be able to carry any part of it anyway. That fuselage part should be designed to carry a forced angular displacement from the wing bending. A very different exercise from carrying load. The pickle fork design carries the resulting (from rib stiffness and displacement) moment to the rib and if the rib is too stiff breaks the fork.