I have always been told the upturned wingtips, blended or otherwise, were to reduce the tip votex's and thereby reduce drag, not to increase lift.

Winglets encourage the vorticity to be shed nearer the wingtips, rather than somewhere else along the span. This produces more lift, since each part of the span contributes lift in proportion to the amount of circulation carried by that part of the span, in accordance with the Kutta-Zhukovsky theorem. In any case, as a general rule, adding a pair of six-foot-tall winglets has no aerodynamic advantage compared to adding six feet of regular, horizontal wing on each side(17).
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(17)This assumes the goal is to produce wings, as opposed to (say) rudders. Also note that the winglet solution may provide a practical advantage when taxiing and parking. This is why Boeing put winglets (instead of additional span) on the 747-400 — they wanted to be able to park in a standard slot at the airport.