Regarding the stochastic parrots:

It is easy to see that LLMs exclusively parrot by asking them about current political topics [1], because they cannot plagiarize settled history from Wikipedia and Britannica.

But of course there also is the equivalence between LLMs and Markov chains. As far as I can see, it does not rely on absurd equivalences like encoding all possible output states in an infinite Markov chain:

https://arxiv.org/abs/2410.02724

Then there is stochastic parrot research:

https://arxiv.org/abs/2502.08946

"The stochastic parrot phenomenon is present in LLMs, as they fail on our grid task but can describe and recognize the same concepts well in natural language."

As said above, this is obvious to anyone who has interacted with LLMs. Most researchers know what is expected of them if they want to get funding and will not research the obvious too deeply.

[1] They have Internet access of course.