The answer is that they are using carbohydrates -- they're just not carbohydrates that have the same glycemic index effect on blood sugar. For example, they're not using refined carbohydrates, added sugars, or high-fructose corn syrup. Instead, they're typically using sugar alcohols such as sorbitol, xylitol, and manitol.
The problem with these sugar alcohols is that they aren't necessarily the healthiest thing you can put in your body if you're doing it in large quantities. Because these sugar alcohols are not absorbed and digested in the same way that sugar is, they can cause digestive disorders. Many people report diarrhea or flatulence from consuming these alcohols. They may also experience stomach cramps.
The fact is, there's no such thing as a sugar ingredient, even if it's a sugar alcohol, that doesn't have some sort of effect on your system. Even these low glycemic index sugar alcohols are still molecularly similar to sugar, and they are still processed food ingredients. I know I have recommended some products in the past based on xylitol, but only those that are designed to be used in small quantities, such as xylitol chewing gum.
I've been horrified to see the quantity of low carb foods that are being consumed by people following the Atkins diet and other low carb diets. Instead of purchasing and consuming natural low carb foods such as vegetables, fruits, and whole grains, they are instead purchasing large quantities of processed low carb foods, such as low carb protein bars and low carb mixes or drinks.
If you're going to eat low carb, what you should really be doing is getting away from all processed foods, including low carb processed foods. You should be turning to food sources from nature, such as nuts and seeds, fruits and vegetables, whole grains, and healthy oils. Or, if you want food that tastes sweet, use a natural herbal sweetener like stevia that won't upset your stomach and digestive system. And remember, the net carbs claims on low carb food product labels may be good marketing, but they're not necessarily good descriptions of what's actually contained in these food products.