>I have this burning suspicion - borne out by my own anecdotal experience - that the most important thing distinguishing the median Harvard undergraduate from the median Good State School undergraduate is a capacity to absorb the tuition fees.

Not true. Even near the upper end, the price tag is not insanely high compared to top state schools --

Harvard policy states that families with annual incomes below $60,000 pay only a student contribution of a few thousand dollars, and families with annual incomes between $60,000 and $180,000 pay the student contribution plus a family contribution averaging 10 percent of annual income.