So if someone builds an atom-perfect artificial brain from scratch, sticks it in a body, and shows it around the world, should we expect the creator to pay licensing fees to the owners of everything it looks at?

That's unrelated to an LLM. An LLM is not a synthetic human brain. It's a computer program and sets of statistical data points from large amounts of training data to generate outputs from prompts.

If we get real general-purpose AI some day in the future, then we'll need to answer those sorts of questions. But that's not what we have today.