Where have you heard that? Whenever I google this topic, it's current articles (not outdated ones) claiming its not great for your car.
I do live in the "Driftless" part of Wisconsin. It's very hilly! When I leave my driveway, I don't get past 2nd gear to climb the first small hill to my neighbors. Even with momentum, I have to drop to third gear to climb one of the hills coming home with my Mirage.
Old & outdated to me is the "old timers" who talk about old vehicles having to climb some of these hill roads in reverse. The fuel tanks were gravity flow & getting fuel to engine meant going up hill in reverse sometimes. The road that I live on is a dead end. At one time it was connected to another road. Since the road had such a still hill on it, they eventually closed it. Thus, making two dead end roads instead. I know of a number of roads in my area that are like that. Thus, I sort of believe the "old timers" stories about climbing them backwards years ago.
I live about 12 miles from the nearest gas station. Squeaking the last mile out of my gas tank isn't a high priority. I don't think a fuel pump has to be totally submerged, but there's a lot of very current information out there claiming it's not good to run car gas tanks low.
Running your tank low is not only bad for your fuel pump, but your owner's manual has this added caution -
"Running out of gas could damage the catalytic converter. If the warning display appears, refuel as soon as possible."
I looked up catalytic converter costs, & this is what I found - "The average cost for a Mitsubishi Mirage catalytic converter replacement is between $907 and $939. Labor costs are estimated between $88 and $111 while parts are priced between $819 and $828."
I am not really sure running your tank empty is really worth it, but good luck to those who think otherwise!