I'm not sure how helpful this is since I have a beater-only XV-11 Neato, but it doesn't usually get tangled in the 'fluffy frayed' 60 - 70mm fringe of a very thick rug - a rug so thick it can only climb onto it at an angle. However, it would constantly get caught and often need help when we had a much thinner rug with an 80 - 90mm long plaited cord-like fringe.
The latter situation was made worse by a nearby couch inhibiting Neato's 'backup and try again' strategy, but it occasionally happened even when it had plenty of space to manoeuvre. Other influences aside, I suspect somewhere around 75mm fringe length is the limit for a non-brush beater-only XV-11.
Neato XV-11 SW 2.0 Board Rev 113 / 3500mAh battery pack installed May 2013