The fuel pump just went out on my '09 Chevy Malibu and my neighbor said that I run the tank too low, because the gas keeps the puel pump cool. When you run the tank too low, it allows the pump to overheat, causing it to burn out quicker. Is there any truth to this?

yes, there is truth to that. BUT dying after 4 or 5 years means probably a problem with that pump anyway.
but it helps to not run too low for keeping it cool and not working as hard.
the more gas you have the more pressure is on the inlet of the pump, so it doesn't work as hard getting up to pressure.

What really kills them is sucking air and modern gas tanks designed for in tank pumps usually have a sump built to contain fuel around the pump. If your pump lasted this long I would not worry about either issue. Things wear out.

I really don't have anything to complain about (other than repair cost). The car has over 110K on it.

Be glad you don't have one of the early CPI 4.3's. They were crapping quite a bit in early-mid nineties.....probably still...

I have heard this too many times over the years, but I'm not sure if it's fact, or urban legend, or maybe only applies to certain cars/years.

I know I've run my daily driver LOW several times over the years and never had any issues.

our modern vehicles, I always make it a game. how close to "0 miles remaining" can I get on the overhead trip computers with the low fuel light on, before I stop to fill up.

I've actually driven several miles on 0 before. and I can almost always put 21-22.5 gallons into the tank that's listed as a 22 gallon tank.

110K+ miles and 10 years later, still on original fuel pump

You got 110k miles out of a GM pump...you did good! I've put more pumps in GM stuff than anything else. I still recommend you don't run around on E as the fuel does help to cool the pump. Running them low occasionally won't hurt them, doing it constantly won't help.