I’ve found that eggs I buy from the store are almost always easier to peel than the ones I get from the neighbor or the farmer’s market, so I definitely think freshness is a factor.
Grey or green on the outside of the yolk is overcooked, in my book.
And it’s just not my book: see here.
Green or gray yolks are a sign of poor technique, IMHO.
Superhal:
Then it could be that the eggs aren’t cooked enough. Do you get the grey film on the yolk after cooking? If the yolks are still bright yellow, they aren’t hard boiled yet.
I boil eggs in two stages. Put the eggs in the pan, boil the water. Before the water boils fully, turn down the heat until you barely get any bubbles. (If the water is boiling too much, the eggs will crack and you will get egg white soup.) Let them simmer for a while, I usually leave them for 15-20 minutes at medium heat.
To check, give them a shake afterwards. Soft boiled eggs will move around in the shell, hard boiled eggs will not.
Seems they’d be way overcooked with that method. Bring to a boil, cover, remove from the heat, let sit for 15 minutes or so.
Superhal:
If you are getting egg whites coming off with the shell, you aren’t cooling the egg. After boiling, let it sit in cold water for 5-10 minutes.
I use the rolling method + under running water method.
I’m pretty sure that’s not the problem I had. I had this problem with hard-boiled easter eggs that had been sitting in the fridge for a few days, so they were plenty cool.
But, I get them nicely peeled.