"Your candidates show that after learning how to solve a problem, they can demonstrate they're able to solve it."

The parent of your post is talking about a situation where they've demonstrated they've memorized a solution to a particular problem, not that they can solve it. And that it was the wrong solution, which they didn't notice. It's that last bit in particular, combined with not being able to adapt or create a solution for the actual problem, that is the hard fail.

I can't imagine my personal interview questions & style are common enough to have shown up on any of these sites, but I have personally witnessed two people (out of a few dozen) who knew only and exactly what was on their school curriculum, but were completely incapable of stepping outside of it. I come at interviews from the point of view that I'm trying to discover what they can do, not what they can't, so when I say that, bear in mind that I didn't hand them a problem and smugly watch them fail for 30 minutes, I actively tried to formulate a problem they could solve and failed. I've also witnessed someone persistently applying a book solution that was the wrong solution to the problem. Perfect depth-first search, but it should have been breadth-first, they couldn't seem to understand my explanation of that, and they shouldn't have put it in a tree in the first place. (It would have worked if the correct search was applied but it was massive overkill. It was something like finding a substring in a string... yes, you can represent that as a tree problem, but you're only making things worse.) They nailed the definition of graph and basically just wrote out the depth-first algorithm as quickly as they could write... but it was wrong, and the moment they stepped off the path they were completely lost.

I also don't do brainteasers like this, I focus a lot more on very practical things, so we're talking more like "failing to write code that can take the string 'abcd,efg' and split it on the comma without hardcoding sizes, either handwritten or by calling library code". I really want to start an interview on some kind of success but every once in a while a candidate gets through that I simply can't find the place to start building successes on at all.

(You have to remember the "evaporative cooling" effect when reading about interview stories. Of the good candidates that even go through an interview process, they do one round of interviews and get snapped up immediately. People who have good-looking resumes but, alas, graduated with insufficient actual skills, interview over and over again. The end result is the average interviwee, anywhere, is not very good. One of the preceding interviews I'm referring to emotionally wrecked my day, I felt that bad for someone who had clearly put in immense amounts of (all the wrong kinds of) work but I couldn't even remotely hire. But there's nothing I could do about it.)

I should also mention I run a style of interview where if I ask you a question and you blast it out of the park in a few seconds, great, you (metaphorically) get full points and then I move on to the next harder variant on it. And I can always make up a harder variant of something we can talk about for an hour or two. If I can't find something you can't blast out of the park in an hour or two, well, unless you're completely insufferable or your salary expectations are something I can't meet, expect the offer shortly. But what you'll be "blasting out of the park" will be something like a full round-trip delivery of a service with code-as-infrastructure and a database and user logins and a solid security design and so on and so on, not solutions to Project Euler problems.