There was a whole article about this recently... I forget where, probably the NY Times. Have you read it? Quite illuminating for me. Didn't even realize there was this whole issue/culture about being low-income + Ivy.
What most of these articles fail to mention is that there are three aspects to the traditional socioeconomic diversity narrative: low income, race/ethnicity, and familial educational achievement. As an Asian American whose parents both had PhDs, I've been in the unique position of having only one of the three factors affecting me.