> where you went to school is directly correlated with your family's household income.
Not sure where you got causation from that statement. Ultimately, it doesn't matter if Yale "means" to discriminate against poor people, but the fact is that if you are poor, you are far less likely to experience a childhood and academic life that will do well against the Yale admission requirements.
I'm sure there is a correlation, but I disagree that it is a causation. Much of the correlation is probably the result of early-life educational advantages for stronger socioeconomic families. That's an unfortunate correlation indicative of a larger social problem, but not indicative of admission to Yale depending on income, as you seem to be implying. The two just unfortunately correlate.