I guess as with most things it just comes back to ego. I don't think I have ever seen a belt "go white" before but I have seen a few that have become naturally tattered. But it think 'Brandon Fisher' had it right, if a belts going to get old through wear it will get very weak at the knot and eventually brake well before the rest has gone white. That said just because a dan grade is young (or hasn't had a black belt for long) and has a frayed belt doesn’t necessarily mean they have sanded it. We have a tradition in our dojo where one sensei will pass a belt on to a new dan grade (not always, just some times), in this way a belt can get very old, much older than the person wearing it.