There's a bit of hyperbole here, though I am largely in agreement based on my interviews. In my interviews experience, it is unlikely that you'd be asked to implement quick sort, but that's because you'll be asked a question that requires realizing that a the question reduces to quick sort (this is how companies can avoid hiring people who just memorize solutions). For instance, instead of being asked to create all permutations of a string and all its substrings, you'll be asked a question that involves analyzing a set that needs to be permuted a similar way (this is my example, not from an actual interview, but I'd say it would count as about a medium level difficult question). If you don't know quick sort cold (or, in the case of my example, how to print all permutations of a string), there's no way you'd be able to program something that requires modifying and adapting these algorithms in 45 minutes at a whiteboard.
And yeah, again YMMV, but you definitely do need to largely solve the problem, so speed absolutely does matter here.
The really frustrating thing about all this is that if the experience causes you to go back, study algorithms, buy cracking the coding interview, and getting incredibly good at these questions, your next interview will involve… detailed questions about ruby syntax, followed by another interview with questions about how the JVM works, followed by another interview with questions about how MapReduce works[1].
Not saying this is good or bad, just that this is how it is, at least at the harder interviews.
Based on the final paragraph, it looks like triple byte does see the market opportunity here. The frustrating moving target of interview questions could correlate very well with what type of programmers a company is looking for. Considering that every interview requires a day (or more) off and a stressful and mentally taxing series of in-person exams, there's only so much one candidate can take before giving up and just staying in his or her job (assuming the candidate is currently employed). So if a company becomes aware of how to align candidate type with interview path, if you can line up with the algorithms style interviews, the person can slowly learn until getting a job offer, rather than experiencing a reset button. I wish them luck with this, because they'd be adding real value to a developer's job search, which isn't something devs typically expect from a recruiter.