Properly validated psychometric tests are valid predictors of job performance (by which I mean objectively and factually correlated with actual work performance), and a properly constructed work-relevant test will be on the whole will be more valid than subjective judgments from most technical professionals. Of course there will be hits and misses, but the consistent application is the key to its use. If you don't consistently apply it, it becomes worthless.
But, let's throw that out of the window for a second because in this particular anecdote I don't think it's relevant. This test they were using seems more like a cultural fit, specifically a person-organization fit test. These tests are less about predicting job performance than they are about predicting organizational commitment and ultimately tenure [1]. Surely we can agree that those things are important too.
But, let's again say that this candidate's aptitude is so impressive that we don't mind an increased statistical chance that his or her tenure may short. The real issue is that legally you are obligated to apply the same set of criteria all of your employees for a given role (not necessarily the exact same position, but comparable positions). If the company is applying cognitive testing, personality testing, drug testing, person-org. fit testing, etc. to one group of applicants, you now cannot fail to adhere to that criteria because it is an invitation for legal liability, however seemingly-spurious.
Having said that, it's important that your selection processes have been validated previously, or at least are in the process of being validated (which provides some protection). I also have a big concern with the linked situation because: 1) it's a cultural-related test, which means the possibility to show cultural-related bias is high and 2) they were unwilling to make language accommodations, which seems unnecessarily rigid when native-level English skills are likely not a core component of the job. Point #1 can be accounted for in some shape or form (at a minimum through a low cutoff score), but Point #2 is more problematic.
Anyway, there is a reason companies adopt "Big Corp" characteristics as the scale. The primary reason is for legal compliance through standardization of process, and the other is that data is supportive of the validity of objective predictors of job success relative to subjective judgments.
I realize I may be opening myself up to some criticism and scorn from HN crowd for seemingly representing "Big Corporate" or acting like a Bob from Office Space, but so be it. Despite what it may seem, there are often smart people using evidenced-based processes driving seemingly asinine HR processes that drive you crazy. And sometimes there aren't, and it's just a big pain in the ass for poor reasons.
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[1] PDF of meta-analytic findings about person-job/org fit: http://nreilly.asp.radford.edu/kristof-brown%20et%20al.pdf