the green ring is caused by a chemical reaction between the sulfur and the iron in the egg, and is accelerated by temperature. how one heats the eggs is completely irrelevant to the green ring problem - over heat / over cook it, get green.
the longer the interface between yolk and white stays at elevated temperature, the more faster you get green rings. so technically-on-the-surface-as-far-as-it-went, the statement is correct - but if you over cook an egg, you'll have green whether it is ice shocked or not.
the chemical reaction will continue after cooking and cooling. take a second egg from a perfectly-cooked-no-green-in-sight batch and put it in the fridge for 24-36 hours. bingo! you got green.
I poke a hole in the air sac / big end, do the water boil - soft or hard or harder-soft for DW - followed by an ice bath and I never have an issue peeling the eggs.