I also ANAL, but as far as I can discern I believe the argument is that "race-neutral" admissions are incompatible with giving favorable treatment to a racially biased group, and legacy students are (presently) a racially biased group. It fundamentally is an attempt to force the court to decide whether the mandate of "race neutrality" is anything more than a fig leaf: if you can be "race neutral" while giving preferential treatment to racially biased groups, it is very easy to follow the rule while still producing a racially biased and non-meritocratic system.
