The point of the story was that classifiers can be right for the wrong reasons and almost inevitably are. At least there’s zero guarantee that the reason for making the prediction matches the human or “real” reason why it’s correct.
LLMs are classifiers, there is absolutely no reason to assume they’re any different, regardless of any reasoning tokens they emit. They do what their handler wants to see, that’s all, and that’s what they’re trained to do.
People often take this as a knock against them. It isn’t, it’s just the reality of neural network classifiers. The results speak for themselves and don’t depend on whether they “actually” reason, but all evidence says they don’t, or at least there’s no special reason why they would.