And way more than 1/6th of America is part of a 'poor family'. Old money is vastly over-represented in Harvard, and even more vastly over-represented in the backbone of the institution.
EDIT: THE FOLLOWING DATA IS WRONG. (I foolishly misread a chart. Leaving this up for continuity, but the numbers are completely off.)
---
No. Only 25% of households in the US have annual income between $35,000 and $75,000. About one in five families in the US is below the poverty line. So middle class students are over represented at Harvard. Students from poor families are only slightly underrepresented, and considering that household income and academic achievement are correlated, it’s actually a testament to their efforts to have socially conscious admissions. The facts do not support your argument. On this you are simply wrong.