His point is that at 6V, the resistor is dissipating more power (power is voltage times current) than the LED.
There are special power supplies for driving big LEDs which use a technology called "switch mode power supply". It uses a trick with inductors to minimize this power loss in the resistor. However, for 20mA, it is probably overkill. If you have a big lantern battery, the thing will last for days pulling 20mA. The incandescent light bulb is probably pulling 5x or more of that current. If you used a switch mode power supply, it might double the time before the battery fails to 10x the endurance of the lamp with an incandescent bulb. However, it is somewhat complicated, and will require special chips or a purchased power supply to do it.
Regards, Bob Monsen