Nonsense. I am a weight trainer, among many, who is on a low carb diet. If you believe that you run out of energy when you run out of carbs, what do you do when you run out of glycogen after twenty minutes? Just stop? Go gorge down another potato?? Of course you don't. The difference between a low carber and a high carber is that the low carber moves right into fat stores immediately, whereas the high carber moves into thier fat stores when thier glycogen is used up after 20 minutes.
Further, carbs give you an inefficient source of energy in that they cause blood sugar spikes and crashes. When you carb up, you actually have LESS energy to work out because your blood sugar crashes later. Whereas a low carber is depending on a steady source of fuel [fat and protein] that does not cause this spike and crash phenomenom.
What is VERY important that most people never even mention, is PROTEIN! [this silly obsession with carbs is mystifying!] If you are exercising, it is very important that you have an adequate protein intake. This helps with the muscle repair and regeneration and also helps with the energy level. You are much better off focusing on protein than carbs.
If you weight lift and do not eat carbs you will feel depleted. Anaerobic exercise does not tap into fat stores, aerobic exercise does.
Weight lifting will raise the bodies metabolism over time but not in the short term.
That is not nonsense, but scientific fact.