It’s true that one of the justifications for race-based AA–and perhaps AA in general–is past injustice to a group. Whether this is a philosophically justifiable position is a somewhat different debate.
A given individual is not necessarily the representative archetype of his “group,” not necessarily personally injured by antecedent injustice, and is not able to rectify what happened to those already dead. Nor, for that matter, will he necessarily even rectify injustices to the living. A wealthy recipient of race-based AA is perfectly entitled to stay within the wealthy class and simply be the beneficiary of some good luck wrt to where the rules are right now.
Race-based AA has no opportunity test, by design. If you correct for opportunity, it’s been shown over and over again that you lose race-specificity for preferences. Within every SES tier, the exact same rank order for races in performance outcomes will emerge. At a top SES tier, blacks will outperform asians in basketball; underperform them in academics. And the discrepancy will be so profound that asians at the bottom of the SES tier will outperform blacks at the highest SES tier. Therefore you need race-only based AA to achieve racial balancing.
Then there is the problem of “group,” even when self-identified. Should “black” be a group that includes a recent Nigerian immigrant from a relatively wealthy background into the same group as a poverty-stricken student from a Chicago ghetto whose ancestors were enslaved? Are recent Hmong immigrants from the lowest social tier of their source country in the same “asian” group with the American kid whose parents are doctors?
These are not fundamentally solvable problems, philosophically. Race-based AA does not “correct” any past injustice since there is no such thing as extending remedy to the dead, nor does race-alone AA attempt to extend an opportunity-based remedy to the living.
What race-based AA does is cosmetically balance outcome by race (and specifically, the OMB-based self-identified groupings). That is all it does, but at the level of society, it is both reasonable and beneficial to achieve that cosmetic balance.
The complaint at hand in the OP accuses Harvard of racial bias, and the short answer is that the complaint is valid. An absence of race-alone bias in the admissions process would result in very lopsided racial cosmetic balance. (At CalTech, about 40:1 asians to blacks.)
So while the complaint is correct in its accusation, the defacto effort to cosmetically balance by race should be allowed to stand. It is incorrect that asians are not taking the place of blacks, and therefore “support” race-based AA while being opposed to anti-asian bias in admissions. A matriculating group has a finite maximum, and is therefore a zero sum game. Without race-based bias, almost no blacks would be admitted to elite institutions, even when their applications are normalized for SES opportunity.