The reason this hard-boiling technique works so well is really pretty simple, but it helps to know a little bit about how eggs work.
Eggs consist largely of protein — mixed with mostly water in the white, or albumen, and mixed with fat and water in the yolk. When the eggs are raw, the proteins are like strands of yarn curled up in little balls. As the eggs are heated, these strands relax and unfold. As they unfold, they bump into each other and link up. (Fun fact: This is why egg "whites," which are clear when raw, are white when cooked — the unfurled, linked-up proteins block light from passing through.)
The higher the temperature, the tighter the linkages, at first getting firmer but gradually getting tight enough that they squeeze out the moisture. That's bad. Even worse, as the egg white warms, it gives off hydrogen sulfide gas and when that gas meets the iron particles in the yolks, it forms iron sulfide, which is what that green ring is made from.
The perfect temperature for a hard-cooked egg is right around 160 degrees (actually a little lower for the white, which doesn't have any fat to lubricate it, and a little higher for the yolk, but we'll settle for an average).