Institutions of higher learning should have broad discretion to consider whatever aspects of an applicant's background they choose in considering whether that prospective student is a candidate that should be offered admission to further their studies. That said, Justice Jackson's thought exercise you shared is antithetical to that purpose, and was a shitty attempt at generating an emotional reaction. Her example is the exact opposite of considering the broad and full experiences of an applicant, focusing on one limited aspect of "family story." In my extension of her "thought" exercise, one of the applicants comes from a family that has broad support in its community, both parents active in the upbringing of the student, and enjoys relative health and well being from a social and physical viewpoint.
To keep it short, let's just say the other student struggles in all those areas but still managed to be positioned as a well qualified applicant to continue the higher learning endeavor at that institution. Which student should be given more "credit?" We don't know in her ridiculous exercise because this additional color wasn't considered as she only disclosed the one emotionally charged issue she wants you to value above all others. It's short sighted and it is why schools should have any latitude they choose to look at the entire picture of an applicant as they see fit to further their mission of education and higher learning.