You got the wrong takeaway from your link.
This is falsified by that study, showing that on the frontier models generalized introspection does exist. It isn't consistent, but is is provable.
"no access" vs. "limited access"
You cannot trust that the model has introspection so for all intents and purposes for the end user it doesn't.
I suspect you’re making assumptions that don’t hold up to scrutiny.
You appear to be defaulting to the assumption that LLMs and humans have comparable thought processes. I don't think it's on me to provide evidence to the contrary but rather on you to provide evidence for such a seemingly extraordinary position.
For an example of a difference, consider that inserting arbitrary placeholder tokens into the output stream improves the quality of the final result. I don't know about you but if I simply repeat "banana banana banana" to myself my output quality doesn't magically increase.