this is correct. typical design is to place the fuel pump in the tank itself, using the gas as coolant. allow it to run too low too many times (i have no idea what that number would be), and it will fail.
It is an old wives tale. Even a gallon, which is empty for many cars, is enough to keep the pump cool. How long is the pump actually running at this level anyway? Not very long. Maybe if you are one of those idiots like I remember in high school that only had enough money for 1 gallon at a time maybe there would be something to it.
I have never had an in tank pump fail on me and I always run the car down close to empty before refilling. All these cars had more than 150K on them and one 225. Current vehicle has about 130K with no problems.