Im not overyly sure myself as it was a 'rule of thumb' (i would not call it a rule) well before I got into the hobby.
I think it has to do with oxygen takup by the fish, waste production by the fish and the ability for the water volume to dilute the fish waste enough so that the bactera living in the substrate can process it.
Ideally if you have more surface area you can have more fish for the same volume. So a 20 Long is better than a 20 High because you get more surface area. Greater surface area means more substrate to hold bactera and it also means higher gas exchange.
for your friend doing the massive water changes reguallry probably was one of his secrets. This would maintain water quality to some degree since he we diluting the dirty water by 1/2 on a regular schedule. Cleaning things with bleach would be fine since it would sanatize them. I doubt he bleached the substrate on a regular basis and thats where the bulk of the bactera live.
Also note that for lets say a 10 gal
tank 1 10" fish is not the same as 10 1" fish. The larger the fish the more waste is produced. Plus a larger fish in a smaller box would cause more overall stress on the fish because of its cramped enviorment.