Just because they're attached to the wing doesnt mean they "reduce" wingtip vortices. They just use them to their advantage to reduce drag.
Usually the vortex increases drag by the downwash it produces. By placing the winglet on the tip, it combines with the free airstream which results in somewhat of an angled flow.
By doing this there is a lift vector provided which acts perpindicular to the local airstream therefore producing a vector that is pointed forward.
Just remember that the winglets still produce a parasite drag penalty and added weight to the wing.
So, I'd say your instructor was right!
(how'd I do tgrayson?)