It is a joke
I was in college at the time and deferments were automatic for anyone with passing grades. Flunking out was the only way you were going to get drafted. They almost never took anyone married and never anyone with children.
I am not arguing the right or wrong of any the college deferments, only the fact that they were routine, required no extraordinary effort and were granted to rich and poor alike. There was no social stigma attached at the time.
May have been different in other districts and the lottery obviously was a factor but that's my recollection on the subject in my area.