Its not flat per se, but it has a specularity, a lack of any shadow, and still gives you depth that I think is the main attraction to ring flash. Especially for fashion designers. It shows clothing very well, and keeps the texture of the clothing which allows the viewer to 'feel' the fabric. And thats important to them in catalog and advertising.
I am very puzzled... except for the first photo, in the OP, I see absolutely no hint of texture in any shots taken with theses lights, in any of the links in this thread! For that matter, it is even hard to see the folds in the cloth as it drapes!
I think what is most important to these designers is to NOT make the model look too attractive, and distract the viewer from the clothes. It does that!




