Wait, I'm confused... Are you saying that it can be illegal to have hiring practices that are suboptimal? For example, you mention that brain-teaser tests might have disparate impact on some applicants--and they're also not that effective anyway.
So if you hire a smaller fraction of any racial category of applicants than there were in the pool of applicants or in the workforce of your region, then your hiring method has disparate impact. If you use an objective test that contributes to that disparate impact, you have to be able to prove by thorough studies that it was the best method to pick staff for the specific job you are hiring for. Such studies start around seven figures and won't work for positions with multiple responsibilities or difficult to measure outputs.
Is it necessarily because of the hiring method, though? Couldn't it be possible that there is something about the company as a whole that causes people in a protected class to avoid applying to the company? (For example, if the company has racist ads.)
"Note that a brain-teaser-type test used in a hiring process (might be illegal if [both] it can be shown to have disparate impact on some job applicants and [if it] is not supported by a validation study demonstrating that the test is related to successful performance on the job)",
not "Note that a brain-teaser-type test used in a hiring process (might be illegal if it can be shown to have disparate impact on some job applicants) and ([furthermore] is not supported by a validation study demonstrating that the test is related to successful performance on the job.)"
As I read the sentence, a general brain-teaser is supported (by all the research showing that tests of general mental ability are predictive), but it is not legal unless you've done a study specifically for that brain-teaser.