A little extra reason to refuel your car sooner rather than later is that the fuel pump will be stressed more as the tank approaches empty.
These pieces of advice are technically correct but catering for edge cases that won't affect 99% of drivers/vehicle owners. Modern cars are designed for the way people use them; people run their tanks to empty all the time.
With the average used car on US roads now over 12 years old, having the pump go bad could mechanically total some vehicles (the repair cost would exceed the vehicle's worth), so you're going to want to prolong it's life however you can.
Another commenter already pointed out the heat issue since the fluid acts as coolant.