[Fishkins]

It's clearly important to be able to communicate about technical problems, but is it really necessary to be able to narrate your thoughts about a technical problem in real time as you're first having them?

In my work experience I don't remember ever having to do that. I'd look at code & investigate a problem independently, then talk to someone about it afterward. I think that should be considered at valid approach to the interview.

[dota_fanatic]

It sounded from the example like the code under discussion was quite simple, "ten lines of code". So it's plausible your "look at & investigate independently" is allowed to happen, and should take less than a few minutes, say, and then this interviewer is inviting them to walk through things in a shared manner.

In other words, from my perspective, you're not actually in disagreement with their method. They weren't saying "narrate in real time as you're first having [thoughts]". Practically nobody does that ever, or is expected to do it, except in other practices like mindfulness or therapy and what have you. They were saying they ask them to understand it, explain it, and then talk about improving it. OP's problem was with the candidates whom couldn't understand the code, and weren't even willing to talk about the state of their understanding so that the interviewer might help them walk through things further...