I think that this might be a nice way of getting round my objection, but there is one worry, which is that X is relative to a distribution on the questions we ask when we aren’t dealing with Encyclopedia Eric but with an LLM. I don’t actually use LLMs very much myself, partly out of arrogance and Luddite tendencies. But I suspect that the value of X for some sorts of questions (simple quiz questions, maybe?) and some LLMs (maybe not Google’s) will be high enough to end up in the murky case.
Of course, both you and I agree that there /is/ clearly a difference. I can see the attraction of appealing to the intuitive or pretheoretic notion of knowledge, since it’s a fairly straightforward way of stating the difference and it’s not obvious how else one might put it (I suppose ‘LLMs don’t explicitly think through the facts stored when deciding what to say’ is one way of putting it.)
I remember some time ago rather sleepily watching John Hawthorne talk about conditionals; my sole memory was of his banging on about ‘the little logician in the brain’ (I think the point was something like: some conditionals seem [in]felicitous in virtue of form because the little logician in the brain is reading them; others seem infelicitous because we examine them more closely and look e.g. at the referents involved, in which case e.g. Gricean considerations apply). One difference at least in the case of LLMs that makes sense to me is that there is no ‘little logician’ in LLMs.