You're using a different definition of "hallucination" than the one most people use when talking about LLMs. If you want to do that that's fine, but you're definitely in the minority.
Yes, it means proper application of the term means you have to know what went into its training data (or current context), but you'd have to make those assumptions anyway to be able to put any credence at all to any of its outputs.
An LLM is doing the exact same thing when it generates output that you consider to be a "hallucination" that it's doing when it generates output that you consider "correct".
Another way of framing it would be along the lines of 'catastrophic backtracking' but attenuated: a transformer attention head veering off the beaten path due to query/parameter mismatches.
These are by no means exhaustive or complete, but I would suggest knowledge exhaustion, stochastic backtracking, wayward branching or simply perplexion.
Verbiage along the lines of misconstrue, fabricate and confabulate have anecdotally been used to describe this state of perplexity.
Like, it's a bit sarcastic, sure, but until factuality is explicitly built into the model, I don't think we should use any terminology that implies that the outputs are trustworthy in any way. Until then, every output is like a lucky guess.
Similar to a student flipping a coin to answer a multiple choice test. Though they get the correct answer sometimes, it says nothing at all about what they know, or how much we can trust them when we ask a question that we don't already know the answer to. Every LLM user should keep that in mind.