Actually it does apply to the speed limit too, there’s a proviso to the speed limit laws dealing with going too fast for the current conditions. Mostly it comes into play during bad weather or in construction areas generally after an accident, the core logic is that even though you were going the speed limit or lower the fact that you hit somebody shows you were driving too fast for the current conditions.
That’s why NC uses “Driving While Impaired” rather than drunk driving. You drink a couple of beers and pop a Benedryl and you still blow under the limit. But you are impaired