You are not necessarily in disagreement with IslaDeEncanta, as they said "lower middle class", not "low-income". What exactly constitutes "middle class", and even "lower middle class" is not clear. But, I think, most would agree "low income" means not middle class, so you're probably talking about different sets of people.
You're right. I wasn't really talking about people in poverty/near poverty. They can benefit from the network involved with an Ivy more than just about anyone, because they usually don't have a network at all.
Everyone talks about the networking but this can't possibly be true for everyone. What if you're just not good at networking? And do poor kids on scholarships get accepted by their yacht-class peers?
My friend had subsidized tuition at Columbia, and IIRC their cutoff at the time (2009-2013) for household income was $100k. If it's a similar figure at other schools, I guess you could decide on some sort of demarcation around there.