Underfire
Why do you claim there is no such thing as wingtip vortices? Would "vortices formed at the wingtip caused by the combination of spanwise and chord wise airflow mixing" be a better description?
I am not saying vortices only form a the wingtip but it is widely accepted this is where they are most prevalent. Any part of the wing trailing edge will have this issue where span and chord wise flow meet, clearly exacerbated by sweep. This in turn increases the downwash, reducing the effective relative airflow which turn affects the total reaction in favour of drag, hence lift induced drag.
Either way, this induced drag is reduced by winglets. The fact that poor winglet design in terms of wing blending can increase interference drag was not part of my discussion or that of the original poster.