I can only surmise what he meant by that statement, but generally speaking, most animals do well with periodic times of fasting. Most animals in the wild will go a certain amount of time without food, sometimes because supply is low, but sometimes because they just don't feel like eating. It's helpful to the system in such cases to have a day to rest and clear itself out. I can only assume the same would go for fish.
I never feel guilty if I don't feed my fish every night, because generally, our tendencies are to overfeed. So, to have a day or so without food not only gives the fish's system a break, but it also helps keep tank pollution down. IMO.