@BlacKnightAgain, we're just dancing around the problem of defining what 'creative' means.
In your specific example, I would argue that it is not, based on my understanding of 'creative.' But that's because it's an exaggerated example, not because it's a meaningful point.
Consider the oft-stated comment 'If one gives an infinite number of monkeys an infinite number of typewriters, one of them will write Shakespeare.' Is that monkey 'creative?' Again, I would argue it is not, because the creativity is inherent in the probability of infinity.
On the other hand, suppose we have a black box which reliably writes new, never-before-written Shakespeare-grade material on request. Is that black box 'creative?' Does it matter whether the black box (of arbitrary size) contains a human being, an animal, a disembodied brain, or a computer? If so, why?
You say 'random mashups of things humans have created.' I can argue (likely incorrectly, but still) that every work of fiction which does not coin new words (and, perhaps, even ones that do) is a 'random mashup of things humans have created.' Humans created the words; authors mash them up. Joseph Campbell makes a moderately persuasive case that there are only a few stories, retold in all sorts of interesting permutations but still, fundamentally, the same story.
Part of the problem is 'random.' Modern LLMs are about as 'random' as many people are when stringing sentences together, and potentially less so. They're not monkeys banging on typewriters.
One step back: is 'West Side Story' creative, or a mashup of Shakespeare? What about 'R+J', which uses Shakespeare's dialogue but is visually extremely different? Creative, or not?
Back to my black box. If one postulates a future AI that reliably emits Shakespeare-grade stories, how exactly does one argue that it is not 'creative?' Oh, you can ascribe the creativity to the programmers of the AI, but none of them can write Shakespeare-grade stories, so where did the 'creativity' come from? Or you can ascribe it to the source material being combined, but that's like saying Degas wasn't creative because he learned everything from studying the paintings of other painters. And, of course, it's also like saying that humans aren't creative. The creativity comes from either God or evolution, whichever 'programmed' humans.
Next, a big step back. There's an interesting intersection of physics and philosophy that holds that the universe is deterministic and predestined (from the instant of 'creation' - presumably the Big Bang), and that free will is an illusion. If so, Shakespeare himself is no more than a biological machine who wrote exactly what he was 'designed' by nature to write, no more and no less. His creativity exists as a byproduct of the exact conditions of the Big Bang.
All of this just chases the fundamental question of what is actually meant by 'creativity,' which was my original point. People use the word, but I suspect it does not mean what they think it means. Without a solid definition, saying something is, or is not, 'creative' is about as useful as saying it's 'pretty' or 'cute' or 'attractive.' It's an eye-of-the-beholder view, not something really subject to factual analysis.
If I, say, pull up the Merriam-Webster definition, I get 'having the quality of something created rather than imitated : imaginative.' If an AI produces something that does not, on a word-for-word level, imitate something, it is 'creative' by that definition, like it or not. It might, in fact, be based on its inputs, but so is 'West Side Story'.
I don't find it the most useful definition, but it certainly doesn't preclude software from being creative. And it will take a lot of philosophy to make either the argument that 'creativity' is either inherently biological or is not, especially when philosophy already considers there to be an open question as to whether any human, anywhere, at any time, has ever been 'creative' at all.
But, if one assumes, for the purpose of argument, that at least some humans are 'creative,' does that say anything about whether machines can, or cannot, be creative? That isn't at all clear to me. We have a reasonable idea of how and why LLMs generate the output they produce (though it is increasingly clear that it is a 'reasonable' idea, even for the top experts in the field, not an authoritative understanding), but we don't really understand how humans generate the output they produce, so there's no prima facia case that we don't produce things in the same way, but using biological computation rather than technological computation.