I never heard of this. As Sadie H. says, the "age" of eggs is more due to the age of the woman, rather than the age within any menstrual cycle. As far as I know, the early ovulation MAY (emphasis on MAY) influence how much hormone is then produced by in the luteal phase of the egg follicle, which affects implantation quality, but it has nothing to do with the egg itself. Even so, you have the opposite - a longer development of the follicle - which in turn probably has to do with the amount of FSH in the beginning. Once you ovulate, the egg is the same, right? You aren't making new eggs month after month.
I don't know anyone who has faced the issue you mention, and I don't see anything anywhere on line from a reputable medical source that says this. There are conversational blogs that talk about it, but it's mostly people asking the question you are asking, not anyone with any medical info.