This is only my opinion!!!!!

Though carb allergy and carb addiction produce the same results, an uncontrollable appetite for carbs and binging, the two conditions are not alike in their causes, physical reactions and necessary treatments.

Carb allergy is a food allergy to a particular class of carbs, i.e. grains, sugars. It is like other food allergies such as dairy and yeast producing foods in that eating the food can cause a reactive increased appetite for that particular food allergen. Carb allergists' physical results, unlike those of a carb addict, can result in bloating, water retension, swollen joints, gas, diarhea, vomiting, mental fogginess and disorientation, skin eruptions and flu like symptoms. As you can see these are all negative symptoms and can make you feel very ill. Low carb diets other than CAD are the appropriate treatment for this condition as they eliminate, minimize exposure to allergens. Generally, carb allergists don't react this way to carb vegetables and fake sugars.
So, yes, carb allergists can not control themselves at a Reward Meal. They are reacting to a food allergen!

On the other hand, carb addicts react to carbs as a group and can have a reaction, yes, to grains and sugars but also to carb vegetables, even broccoli! , and fake sugars. A carb addict's physical results, unlike those of the carb allegist, include pleasure and a sense of satisfaction and not the negative physical ones above. In addition, the carb addict can feel sleepy, lethargic and drugged. But that is the point. Carbohydrates are a drug to the carbohydrate addict. Think of a heroin addict. He gets a high when using the drug but as time goes on the pleasure period gets shorter and requires higher doses and more frequent applications to attain. The same is true of a carb addict, except where the heroin addict cycles over a period of time, the carb addict cycles many times in a day. In fact every time he/she eats or eats carbs.

So you can see that you have physical reactions, i.e. craving and binging, that are the same in both cases but their underlying causes and treatments are very different. Put a carb allergist on CAD and it won't work for them. At the same time, putting a carb addict on Atkins, other than the induction phase, or one of the more moderate low carb plans won't work for them either.

I think one of the determining factors in answering the question "Carb allergy or carb addict?" is the person in question's reaction to fake sugars and sugar alcohols. Consuming fake sugars and sugar alcohols seem to bother only "true" carb addicts (my feeling ). A "true" carb addict reacts to anything carb or carb tasting, while carb allergists react only to their specific allergen(s). Another sign of a carb addict is an increased appetite or carb craving resulting from eating more than four times a day.