AIUI it's fairly well established that the models can be saying one thing and "really" thinking another anyhow. The ones I recall seeing traced how simple one-digit arithmetic was done in the chat versus the actual activations under the hood. Tracing a real, non-trivial task through that way would be challenging, and I'd expect it is unlikely that the reasoning would say one thing while some utterly unrelated actual thought process is happening below, but I would expect that there might be a lot of places where the text of the reasoning diverges from what is "actually" being done. I'm not sure the full reasoning readout would produce much real insight anyhow.

I suspect that in some decades, as other architectures are found and used, that the inability of an LLM to "think" without also emitting a token will be seen as one of their fundamental limitations.