Yes, and it makes sense if you think about it. Unless you also want to increase your daily caloric intake, as you increase your carbs, something else needs to decrease. You can only eat so little protein and not be getting enough, so it's usually the fat that decreases.
By the time you reach maintainance, you will be eating a wide variety of veggies and a pretty good quantity of them as well as some fruits, nuts, perhaps some whole grains, adequate protein and healthy fats in the amounts that you can have and maintain your weight. Dr. Atkins calls this the Atkins Carbohydrate equilibrium or ACE. I doubt your neighbor would find this unhealthy unless they are still parroting the old "fat is bad, carbs are good" dogma.
OTOH, they may be mistakenly thinking that everyone who does Atkins stays at 20 grams of carb for the rest of their lives which is a common misperception. Most people find that they can maintain between 40-60 grams of carb per day and many find that they can maintain at higher levels. That's a lot of room for veggies, low GI fruits and even some whole grains in moderation.