I use a sling. In regards to the argument, I would have thought that mounting a camera on a tripod in portrait (90 degrees) would have put more pressure on some parts of a camera (the parts above the thread) and would be more stressful than hanging upside down where the weight is distributed more evenly.
Also, it's not designed just for tripods. Battery grips also thread in there. (And I'm sure plenty of people hold their cameras solely by the battery grip whilst walking around as well). Can't see how it's any difference holding your camera by a battery crip vs a sling.
I did recall reading one story about a Nikon user who damaged their camera and Nikon wouldn't supply under warranty which may be where this rumor originated from? Seemed like it was a camera fault (considering how many Nikon users would use slings).