I have to disagree. I think it has much more to do with the fact that elite schools sit on more money than they know what to do with, and can (and do) give it to the students who need it most. They play a different game than state schools.

The state schools have a limited amount of money to work with each year and have to shepherd their resources each year. The Harvards and Yales of the world don't need to worry about money (considering they a $30 and a $19 billion endowment, respectively) as much in the short term and can take a loss on tuition for a bright student, knowing that most of their graduates will go on to be successful and contribute back to the school.