It’s the exact opposite, in fact. Fresh eggs are generally much more difficult to peel than eggs that have been allowed to sit in your refrigerator uncooked for one to two weeks.
Q.E.D’s Perfect Hard-cooked Eggs:
Fill a pot with sufficient water to completely cover the eggs and bring them to a boil on high heat. Once boiling, immediately cover the pot and remove from heat. Allow the eggs to sit for 15-20 minutes, then dump out the hot water and fill the pot with cold water. Allow the eggs to sit in the cold water for about five minutes, before draining.
Cooking them this way rather than boiling them makes the whites softer and less rubbery, and prevents the surface of the yolk from turning that unappetizing greenish grey color.