You absolutely can be too poor to attend Harvard or any school that uses parents' financials to determine whether YOU are deemed eligible for financial aid. What those schools believe your parents can pay may not mesh with what they believe. They may not want to pay anything. Some cases I've seen are with remarriages, where a well to do step parent refuses to pay, and the parent doesn't have the resources. Too bad. If a NCP is involved and s/he refuses to pay, too bad. If parents refuse to fill out the aid application, too bad. It's worse to have parents with means who refuse to pay than parents who cannot afford to pay in the situation where a kid is accepted to such schools. The schools have no merit awards most of the time and your parents have to qualify for financial aid, not the student before any money is given.
I have a friend who retired very early and put all of his money into investment properties. Family lived off of the net rent and he figured the increase in value of the properties would be what would fund his old age. To sell a property meant to reduce the income and tax breaks that the property generated. Harvard didn't care. Didn't get any money at all. Owning a business means that you have to go by the way the colleges assess the business and they also add back expenses that one can deduct.
So yes, there is a large category of kids who are too poor to attend Harvard.
Visit. There is a different vibe to each school. If you could not afford to do so, or are financially hard pressed so it isn't wise to do so, that would be one thing, but you are shrugging off a $50K differential, so pay up 10% of this to take the trouble to feel out the places. I say so because there really is that much difference in the atmosphere of each of the choices. Some of my kids took that very much to heart. Two of them knew they had "come home" at a certain college, and that went a very long ways in their happiness and determination to make things work out when things did not go well. So do your research and go there I know kids who love, love, loved Bard. It was just what they wanted. Others who ran the other direction after a few minutes there. Some who felt W&M (my favorite of the bunch) was just the perfect school or like my one son, face swelled up (pollen allergies) and it became clear he'd need aggressive therapy in the way of shots. Kind of a deal breaker. Too bad, i loved the school and the flowers that rivaled those at some botanical gardens. My son also visited TUfts where my DH was gung ho and felt it was the perfect school, Boston, great rep, great academics, and my son really did not like the feel of the kids there. So, yes, that can go a long way in picking a school. Some sorts that love Bard's quirkiness, WM's more traditional feel, Brandeis's Boston, and Macalester's LAC specialness, may not like other attributes of that group at all.
If it's all good, lay down what it would cost--minus loans and workstudy, take those out of the awards, each year, and offer up half to your kid. $25K in a nest egg at grad can cover a lot of start up costs, some travel, start a savings or brokerage account, pay for great car in full. YOU save your part too, and that will give you options at the end of this ride, not to mention fund the rises in cost that will come up as well as emrgencies.
I know kids at and were at all 4 schools who love them, hate them.