In general, if someone wants you to improve minority representation, you can assume they don't trust your personal judgment

I don't think this is true. The doctrine of disparate impact says that your personal judgement is irrelevant -- you MUST achieve something resembling proportionate representation regardless of anything (other than a demonstratable business need). It tests for outcomes, not intentions.

Did you notice you were objectively wrong about the reason you gave for your speculation?

I'm still confused by this part. By 'legally approved', I'm referring to the state of things in, say, Chicago, and doing decisions by lottery is an easy way to satisfy both disparate impact and disparate treatment requirements.

By 'legally disapproved,' it sounds to me like the part you quoted is obvious that this is disapproved. But let's take a closer look at the actual decision (copied from a pdf, so there may be errors caused by my reformatting):

Before proceeding to the legal analysis, I offer a brief word about the Supreme Court’s recent decision in Ricci v. DeStefano, 129 S. Ct. 2658 (June 29, 2009). I reference Ricci not because the Supreme Court’s ruling controls the outcome in this case; to the contrary, I mention Ricci precisely to point out that it does not. In Ricci, the City of New Haven had set aside the results of a promotional examination, and the Supreme Court confronted the narrow issue of whether New Haven could defend a violation of Title VII’s disparate treatment provision by asserting that its challenged employment action was an attempt to comply with Title VII’s disparate impact provision. The Court held that such a defense is only available when “the employer can demonstrate a strong basis in evidence that, had it not taken the action, it would have been liable under the disparate-impact statute.” Id. at 2664. In contrast, this case presents the entirely separate question of whether Plaintiffs have shown that the City’s use of Exams 7029 and 2043 has actually had a disparate impact upon black and Hispanic applicants for positions as entry-level firefighters. Ricci did not confront that issue.

The Ricci Court concluded that New Haven would not likely have been liable under a disparate impact theory. See id. at 2681. In doing so, the Court relied on the various steps that New Haven took to validate its civil service examination. Id. at 2678-79. It is noteworthy, however, that in this case New York City has taken significantly fewer steps than New Haven took in validating its examination. The relevant teaching of Ricci, in this regard, is that the process of designing employment examinations is complex, requiring consultation with experts and careful consideration of accepted testing standards. As discussed below, these requirements are reflected in federal regulations and existing Second Circuit precedent. This legal authority sets forth a simple principle: municipalities must take adequate measures to ensure that their civil service examinations reliably test the relevant knowledge, skills and abilities that will determine which applicants will best perform their specific public duties.

In rendering this decision, I am aware that the use of multiple-choice examinations is typically intended to apply objective standards to employment decisions. Similarly, I recognize that it is natural to assume that the best performers on an employment test must be the best people for the job. But, the significance of these principles is undermined when an examination is not fair. As Congress recognized in enacting Title VII, when an employment test is not adequately related to the job for which it tests—and when the test adversely affects minority groups—we may not fall back on the notion that better test takers make better employees. The City asks the court to do just that. Regrettably, though, the City did not take sufficient measures to ensure that better performers on its examinations would actually be better firefighters. Accordingly, the court grants the Motions for Summary Judgment and finds that Plaintiffs have established disparate impact liability.

What does this say? In effect, that any test which has different score distributions for different races is guilty until proven innocent. They go on, in sections II and III, to discuss the numbers and conclusions of the calculations.

However, the general cognitive factor exists and differs by race, and will show up on almost any cognitive test. As a result, every test is guilty.* This is the reverse of good sense- the military has done copious research to show that, for every job, g is beneficial (see here for discussion, references to other research, and so on), and the only question is how beneficial.

*They imply that if the Ricci history had been different- that is, the city had promoted the white firefighters on the basis of a rank-ordered written test, and then the minority firefighters had sued on disparate impact grounds, the minority firefighters would have lost because the city had put in sufficient effort to validate the test- but that doesn't seem like the sort of thing that should be taken on faith. Indeed, one of the arguments in the decision,

In essence, the City asks the court to reject Plaintiffs’ statistical significance analysis because it improperly assumes “perfect parity” among groups of people (see Def. PF Mem. 1-3, 5-7)

is responded to by:

First of all, the court rejects the premise that comparison to a standard of equality among groups provides an improper foundation for statistical testing under Title VII. In order to determine whether a particular employment practice has had a disparate impact on a minority group, statistical tests “ask what the results would be for the salient variable . . . if there [had been] no discrimination.” Adams v. Ameritech Servs., Inc. , 231 F.3d 414, 424 (7th Cir. 2000) (emphasis added). To determine what results “would be,” statistical tests properly assume that racial or ethnic groups will perform equally well absent discrimination.

The only two possibilities the court considers is that either the minorities all got really unlucky on test day (stupendously unlikely, as they correctly calculate) or the city is discriminating against them; the possibility that they might not be as good at doing the job (and thus not as good at taking the test) is assumed to not be the case.