Wrong.
It probably does depend heavily on the era you are talking about ... but if you don't believe that some qualified black applicants were given the chance to attend college, that they would have otherwise been denied because of their race - then you are ignorant of this country's history. Just like Thurgood Marshall before him, Clarence Thomas would have had to attend an all black law school if he had been born 20 years earlier.
But if Justice Thomas was looking to attend an Ivy League law school today and was a below average male swimmer he could just identify as Claire Thomas and would be a slam dunk for admission .