If by negative reinforcement you mean hanging a dog, using a Prong, choker, zapping it with an E-collar or shaking it then your quote that's just not completely true.
At best it's acceptable depending on the "community" of training one is involved in. Hunting, Schutzhund, Civil PP, Obedience Comp. maybe, Therapy, Service dogs, Agility, no...not so much.
Now if if you might mean Negative re-enforcement via ignoring the dog holding back praise, ball or food yes I agree and I use that approach.
As far as "Old School" I learned that way 30 yrs ago. I reject those methods as I prefer the Sirus method and that's the style I train in. I want my dogs to "execute" commands because they want to not out of fear of punishment.
I hunt myself and among other this have hunted hawgs in Tn. the traditional way. I do understand the challenges with working a pack. However, all animal training is ultimately Stimulus/Response. It's really only a matter of which stimulus you choose to present to the dog.
Someone who knows what he's talking about!
I don't train my dogs to execute commands because they're fearful of what may happen when they don't, they execute commands because they receive praise and positive reinforcement. Most of them want to obey of their own free will, not because they're afraid I'll punish them.
I am not referring to prongs, shock, choke, etc, etc. I don't use those methods as I know when abused they can lead to long-term behavioral damage of the dog in question.
When referring to negative reinforcement, it is exactly as you say, withholding of rewards, scoldings, and in the extreme cases a "slap on the wrist." Punishing the dog when it does something it's not supposed to do, not punishing it because it didn't do what you want it to do.