The financial aid available at top-tier schools is very generous, because so few low-income students make up the undergraduate body. If I recall correctly, at the top 120 colleges in the United States, only 3% of the student body come from families in the bottom quintile of household income.
As a result, schools such as Harvard[1] and Stanford[2] pay for all tuition for students with a household income of less than $60,000.
Right. Which means that if you are a lower-income student with the academic chops to make it into Harvard or Stanford, it very much behooves you to go. You get a fully subsidized education, and it probably makes much more of a difference to your bottom-line earnings than if you were a child of upper-income parents that's always figured you were going to Harvard.