No, you can't argue with ohms law. The illustration had nothing to do with the Twist or the LT. It was an example of the disadvantage of trying to simulate high voltage vaping by using a low resistance load. Regardless of what circuits they use or don't use, all else being equal, low voltage/low resistance draws more current than high voltage/high resistance to achieve the same power.
Sorry, Ctor doesn't argue with the Omhs law, he relies on it. You do. When some voltage transformer increases the voltage the current in the primary circuit will be proportionally higher than the one in the secondary circuit. To illustrate this let's do some imaginary experiment. Assume VV can produce not 4V but 400v. Atomizer resistance is 200 Ohm. The current in the atomizer will be 2A, wattage is 800 watt, this is approximately like coffe maker consumes. What you say is the current in the battery will be the very same 2A, so 1000Mah battery will last half an hour. You in fact say that one 1000 mAh battery can boil half gallon of water for half an hour. Make output voltage 40000 V and it can drive a car for half an hour? Sorry, laws of physics. perpetuum mobile is impossible. So with the same wattage, high voltage PV will drain battery as fast in theory as low voltage PV. In practice even faster, as some energy will be lost in the transformer itself.