I think you are the one dismissing evidence. The valid chains of reasoning you speak of (assuming you are talking about text you see in a “thinking model” as it is preparing its answer) are narratives, not the actual reasoning that leads to the answer you get.

I don’t know what LLMs are doing, but only a little experimentation with getting it to describe its own process shows that it CAN’T describe its own process.

You can call what a TI calculator does “thinking” if you want. But what people are interested in is human-like thinking. We have no reason to believe that the “thinking” of LLMs is human-like.