Is it possible for quadruplets to get large amounts of aid from top 20 schools?

Perhaps they were just referring to the automatic full rides listed at http://automaticfulltuition.yolasite.com/ . Some of the schools are historically black ones like Tuskegee, Florida A&M, NC Central, and Prairie View A&M. Note that there are also some non-HB schools with automatic full rides in that list, such as Louisiana Tech.

Best would be to check the scholarship web pages of the schools in question to verify that the verbal promises are actually backed by something in writing.