The decision, issued by Judge Beryl Howell, stemmed from computer scientist Stephen Thaler’s efforts to copyright an image he said was created by an AI model, identified as Creativity Machine. Thaler claimed that as the owner of Creativity Machine, he was entitled to the copyright. The Copyright Office rejected that application on the grounds that human authorship is necessary to secure a copyright, prompting Thaler to sue.
Howell ultimately upheld the Copyright Office’s decision, citing long-standing precedent about human authorship. “The act of human creation — and how to best encourage human individuals to engage in that creation, and thereby promote science and the useful arts — was thus central to American copyright from its very inception,” Howell wrote. “Non-human actors need no incentivization with the promise of exclusive rights under United States law, and copyright was therefore not designed to reach them.”
It seems that AI without human guidance is mostly useless. So far we've seen that you need a human operator, and typically one with decent domain-specific knowledge/skill to get an AI to produce anything worthwhile. That guidance is essentially human authorship.
Most of the time, human guidance occurs before the AI generates anything. For example, ChatGPT was trained with human involvement, but most of what it writes will not be reviewed and edited by a human.
However, an identifiable component of the text must have been written by a human author in order to claim copyright. So most of what ChatGPT writes cannot be copyrighted. It would only be eligible for copyright if a human reviewed and edited what ChatGPT had written.
There is an underlying tension in that copyright is explicitly meant to be an incentive for creative efforts made by humans (who would otherwise be doing something else), and AI is generally designed to replace humans engaged in creative efforts.
I wonder to what degree a human would have to be involved? Like if an AI generated the background and you painted on top of it would that be enough. If so, how much would you need to modify the generated output for it to be considered human authored, just changing the colours, some editing/blurring/cropping. Will be interested to see if this gets clarified.
At that point, what is the point? These creative AI are being pushed to replace workers, not work with them. If you have to pay for the AI, and pay people, why not just save the money and use people?
I guess for the same reason you pay for computers but still staff. It's a force multiplier. I think we are still a bit of a ways off from total replacement but the force multiplier effect is something that can happen right now with current capabilities.
As a designer, there is a limited purpose to use generative graphics as assets in a composition for various purposes. I might want to generate a cloud background, or perhaps a small object to use here or there. Certainly not an entire composition, because they always come out bizarre or warped, or having some sort of weird hallucination in them. But generative AI can create, for example, a flower, or a building to be used in background, or to cover up an empty space. Once you place that item, then I would have to go in and touch it up a bit to make it look like it fits and adjust the lighting and fix any weird quirks that might have, but it’s a lot better than having to have a photographer go out and take a photo of it or to pay for a stock photo of it and license that plus every problem that comes with that.
So generative AI tools in Photoshop, for example, can end up saving a lot of time and effort and money for licensing stock photos, especially when I only need a portion of it, but it doesn’t comprise but a small portion of an entire composition. 
You need to exert creative control over the product. If you created an appropriate image for the background, that would probably be enough. If you slapped the same decal on everything produced by an AI, that would probably not be enough.
Remember, AI generated work is in the public domain. So your question is identical to "Can I take a public domain work and alter it sufficiently to claim copyright on the product?". The answer is yes, provided you make sufficient changes.
Remember, AI generated work is in the public domain.
That hasn't been determined yet. A human prompt used by the AI to generate content might be enough to grant copyright. This case is about autonomous AI generated content.
What if I were to create a training model made exclusively from my own artwork. It would only be reassembling my work, so would that not be copyrighteable?