The Court can decide because that’s the law … Title VI of the Civil Rights Act of 1964 prohibits federal funds from supporting activities in which discrimination on the basis of race, color, or national origin occurs. It was passed to prevent schools, hospitals, etc. from discriminating against African-Americans. Currently, the Supreme Court has held that many “affirmative action” programs as currently constituted which take race into account do not violate Title VI, but those rulings are what are being challenged by Fisher.
An institution is free to discriminate on many other grounds. They can discriminate on the basis of intelligence, academic achievement, ability to dunk a basketball, or legacy status. There’s no law the prohibits that, and colleges do it all the time. Nobody has said that Duke basketball has to be “no cut” 
Also, as a partial correction/comment on @tiger1307’s post #29, Section 603 of Title VI appears to give private parties the right to sue Federal agencies to compel them to act in accordance with Title VI (or in this case, the Supreme Court’s hypothetical interpretation of that statute). Also, if another county clerk (not Kim Davis) refused to issue same-sex marriage licenses I think most people would colloquially characterize that as “defying” the Court’s decision even if it’s that’s not technically correct terminology. However, I am not a lawyer.