Among the top-tier CS schools, there's a mix of private and public. Several of those private schools (MIT, Harvard, Princeton, Stanford, etc.) have extremely large endowments that help make college affordable for those that get in.
If you fall in the dreaded "middle-ground" for financial aid, your options for an affordable education are somewhat more limited, but nonetheless existent.
A rough estimate for the United States could be that ~30 states have good to excellent public universities.
The group that seems to be in the toughest spot are the students from states without excellent public universities and in a bad financial position for aid or grant money.
I wasn't just talking about the cream of the crop.
If you can't get into any of the private schools that will satisfy all of your need, and you're not willing to make up the difference on debt, there are many excellent public schools, (Berkeley, UCLA, UMCP, Urbana Champaign, the list goes on), none of which have very high tuition.
Saying that some 1% of kids can get an affordable education at top schools is really quite irrelevant.