They can probably afford to have x% poor kids every year because the rich kids who pay can make up the rest.
If they got masses of applications from bright poor kids every year they would have to be more selective about offering aid.
And just to add another point of data: I did in fact get more grants than the cost of attending, so I profited from attending school without having to work. These policies are very real, and at least to me, they were very transparent and are what made me apply.
I don't think there is any attempt to hide it, either: I think the sad reality is that it's just harder for low income students to compete with upper middle class and wealthy kids who attend the nation's best K-12 schools and whose well-educated parents have pushed them academically as best they know how. Ivy League admissions policies try to correct for some of this, sure, but I'm sure it's extremely tough to balance that with penalizing kids who are well prepared due to their wealth. And these kids are astoundingly well-prepared, as I learned in college.
Why would you be worried about taking out a loan for an Ivy League education? Assuming you don't do something foolish like major in Medieval History, it's one of the safest, strongest investments in yourself you could possibly make, even purely from a financial point of view.
I came out of MIT with something like $40,000 worth of loans, but the M.Eng. that paid for returned (and continues to return) a substantial multiple of that.
It's nice that these elite institutions are now offering an essentially free education for lower middle-class households, but if you feel capable of exploiting the value of such an education, there's rarely a reason not to leverage yourself for it.
Still, though, I absolutely would not have taken out a $200k loan :) that was like 5x my parents' combined income. No way I could stomach that, and I don't understand how others can. I lucked out in studying CS and graduating during a boom so I'm earning quite a lot more than I ever thought was possible, but it was never my goal to be rich, and my state's flagship school was free for me due to merit scholarships.
And, despite following this line of argument, I've been unable to convince my younger sister to apply to Ivy League schools thus far. She's got time left in high school, so it's not final, but she's been balking at the idea of even applying, in part because of the perceived cost, even after I explained the "no loans" stuff to her.