That's not my understanding of the Bakke decision. As I recall, the justices decided in Allan Bakke's favor (5-4) but left other questions open concerning affirmative action admissions practices. Most of the justices wrote their own opinions, which all differed, sometimes in major respects. There was nothing "racist" about the decision itself but it was quite narrow and left lots of room for further controversy over race-based admissions policies -- just the kind we're seeing at UM. In the wake of Bakke there have been a bewildering array of AA court decisions at all judicial levels that contradict eachother and create immense confusion. The USSC needs to lay it down definitively and do so now so that this festering issue can finally be laid to rest.
Ever since Bakke, universities have adopted systems of racial preference that were not as open as the University of California's quota, and which claimed to be aiming at Powell's goal of "diversity." Because Powell's was the deciding vote in Bakke, they often pretended his opinion was the opinion of the Supreme Court, which is not, strictly speaking, true.