I can’t tell if this was a made up story, or based on any truth. The argument is very weak — it doesn’t have to be like the 50's for someone to be more privileged.
That said, I don’t necessarily agree that any race is more privileged than another. I believe that opportunity is broad and bountiful, that a person can elevate their class status with enough hard work, dedication, and/or talent; that doing so will change the lives for themselves and their kin.
A more factual story could be to see what the students’ SAT scores are and really determine if Asians and blacks had a huge disparity. Privilege you can see is much different from privilege remembered from a bygone era.