Who told you that crap? Carbs have little to do with recovery. When we exercise, we breakdown the muscle and break amino acid chains - only protein and sleep help with recovery. By eating protein, we add back in the amino acids to the muscle belly, therefore completing the brached (broken) chain - this is what increases the size of the muscle. Proper sleep is extremely important with recovery. If you are lacking adequate sleep, you will never fully recover.
Carbs are needed prior to exercise for muscle glycogen and ATP production, not for recovery. You need them after you workout to add back the muscle glycogen that you used in the gym. That's it in a nut shell for carbs. They do help with gains, but mainly in water weight and calories.
Keep your diet clean with good proteins and fats, limit the carbs and make sure you get enough rest between workouts.
