Harvard actually does give completely free tuition, room & board, and books—not structured as loans—to anyone whose family makes under $65k/year. Expected family contributions (which may come in the form of loans) only kick in above $65k. Admittedly, that's unusual, only possible because Harvard has a gigantic endowment.
They also want a rather remarkable amount of (expensive) paperwork sent to them. Everything about the SAT costs money, $50 for the basic test, $11 to send the scores to a school (seriously, $11? In 2013 it costs $11 to shove some digits somewhere?) although all is peppered with "fee waiver available".
Aside from the cost investment, there is also the time investment problem. As per above if you decide you can't afford it, and they want a fairly large amount of work done to apply, even if even more paperwork could result in it being free, well, why bother?
My brother went to Harvard, partly because their financial aid offer was best, and I recall my father cursing the required forms. He's a lawyer, so ordinary legalese doesn't phase him, but he found those troublesome. Now I imagine a family without a JD in it, or even without a BA in it, trying to fill them out...
You do not know that. You simply do not. The kids/family are operating from a fear reaction. Some years ago there was a study about why more poor people have (pre-video on demand) cable TV than phone. The paper's conclusion was you could predict and budget the cable bill to the penny, other than traditional low yearly increases, but you can never predict next months phone bill, all you need is some 900 number calls or lots of long distance (back when that was expensive) and that means you literally cannot afford to pay the bill this month, hit to credit report, collectors calling, maybe disconnected (so why bother connecting to begin with...). Whoops. Plenty of poor families can survive a stable $25 cable bill every month for basic cable but not a phone bill that might semi-randomly be $10 this month and $125 next month. Therefore out of fear sign up for the devil you know rather than the devil you don't know.
"No crippling student loans" You sure about that? Guarantee that no aid package to any poor kid in the country would contain loans as part of the package? That is definitely not how it used to be. In the old days you'd absolutely have loans as part of the package. If you get a $125K/yr software dev job, $20K of loans is small, but if you are one of the majority who drop out, or get a financially nonviable degree in a field with high new grad unemployment, that kind of loan could destroy you and your family. Much safer to go to state-U.
What you meant to write is something like a $40K/yr family can send a kid to a $60K/yr school and get a completely unknown and utterly unpredictable but probably rather large amount of help which might even approach the total cost of attendance but you'll never know until you sign up and it might vary from year to year and certainly will vary from school to school. Its not unusual for a low income family to have roughly 100% of their income already budgeted and no substantial access to loans, so teasing the family with $57K of "help" at a $60K school is useless if the family can't scrape up $3K extra per year. If they could scrape up $3K/yr they would probably already spend it on health insurance, or maybe car insurance, or food, or dentistry, or ... So assuming there's an infinite pool of available cash is unrealistic. On the other hand if state-U wants $4K but guarantees loan availability, the kid seems infinitely better off going to state-U because the tuition bill can actually be paid (with a loan ... but paid nonetheless)