The question isn't about universal novelty, but whether the prompt/context is novel enough such that the LLM answering competently demonstrates understanding. The claim of parroting is that the dataset contains a near exact duplicate of any prompt and so the LLM demonstrating what appears to be competence is really just memorization. But if an LLM can generalize from an elephant mirror test to an LLM mirror test in an entirely new context (showing pictures and being asked to describe it), that demonstrates sufficient generalization to "understand" the concept of a mirror test.

I'm not sure what you mean by "genuinely." But in the coding context LLMs answer novel questions all the time. My codebase uses components and follows patterns that an LLM will have seen before, but the actual codebase is unique. Yet, the LLM can provide detailed explanations about how it works, what bugs or vulnerabilities it might have, modify it, or add features to it.