> I do find it remarkable the extent to which knowledge workers are discouraged from sitting and thinking about stuff.

That's such an uncharitable interpretation of the post.

It's a job interview, not a final exam. You're not supposed to sit there thinking for half an hour in order to produce a flawless solution. Maybe the interviewer was making progress, maybe they completely misunderstood the scope of the problem, who knows? The interviewers can't read your mind. Ask clarifying questions, make sure what would be the output of the algorithm in simple cases, then think about it enough so you can outline a solution.