After reading the link info [#221] it appears to me that Boeing strengthened the mid and outer wing but did not make any structure modifications to the inner wing or wing center section.
[made the outer wing stronger which had the effect of transmitting more wing loading into the wing center section that was not modified]
I may be stupid, but I don't see how the wing load is greater with the winglet. The load is aircraft weight and g loading; that hasn't changed. I can see stiffening the wing tip as the winglet is increasing the local loading, but the final load carried by the wing box is constant. The wing load profile will change, but not the total load.