You are right. There is no free lunch. The battery is not a primary source of energy, it is a storage device from energy provided by another source. So there has to be an external source of energy of some kind. Once the car is started, is is using battery power with losses, and there is absolutely NO WAY to recover the losses to heat, friction, etc.
They simply haven't explained what the primary source of energy is yet.
It is NOT energy that started in the battery, then was somehow pumped back into the battery, after having provided the energy to move the car.