Sycophancy and flattery are words that relate to how humans experience LLMs. It's appropriate to use words that could anthropomorphize as descriptors for a problem when that problem exists in the space of human experience. It doesn't matter that an LLM is merely a predictive model. It matters that humans who use the model perceive it as a conversation partner and walk away feeling 'flattered' by the model's predictive responses to the humans' input, which the model predicts without regard for factual accuracy, which happens in turn because (as you point out) "there’s no contradiction from the point of view of the model."
We could call the problem "LLM predictive output which tends to have the effect of flattering the user's opinionated assumptions without regard for factual accuracy" if you prefer that much of a mouthful, but "sycophancy" describes the problem well and is one word instead of twenty.
> One prompt will elicit a response based on one set of weights that are most closely related to the prompt. A different prompt will elicit a response from a different set of weights, for the same reason.
Yes or, in other words: there's sufficient contradictory data which were used to train the model's weights that it will predict (a series of tokens which when read in order in English convey) accurate information for some prompts and (a series of tokens which when read in order in English convey) inaccurate information for others. That the contradiction is beyond the LLM's scope is part of the problem. The two identical parentheticals above are (or ought to be) as unneeded as pointing out that a statistical model cannot technically be sycophantic.