The fasting thing came about because big kennels like hunt kennels or gundogs used to give the staff a day off on Sundays, and the master wouldn't bother to feed them.
Dogs in the wild don't fast by choice, they kill and eat when food is available, sometimes more than they need, so don't feel hungry for a few days, or they go hungry some days because there is no food to catch.
Mine wouldn't let me 'forget' to feed them although they do get fed at odd times, especially if I am out all day travelling to a show.