[HarHarVeryFunny]

I think the more general/useful definition of "hallucination" is anytime the LLM predicts next word based on "least worst" (statistically) choice rather than based on any closely matching samples in the training data.

The LLM has to generate some word each time it is called, and unless it recognizes soon enough that "I don't know" is the best answer (in of itself problematic, since any such prediction would be based on the training data, not the LLM's own aggregate knowledge!), then it may back itself into a corner where it has no well-grounded continuation, but nonetheless has to spit out the statistically best prediction, even if that is a very bad ungrounded prediction such as a non-existent API, "fits the profile" concocted answer, or anything else ...

Of course the LLM's output builds on itself, so any ungrounded/hallucinated output doesn't need to be limited to a single word or API call, but may instead consist of a whole "just trying my best" sentence or chunk of code (better hope you have unit test code coverage to test/catch it).