No, you are wrong about this.
See:
https://technophilosoph.com/en/2025/02/07/ai-prompts-and-out...
If you have a more recent citation referring to case law that states the opposite then that would be great but afaik this article reflects the current state of affairs.
The human using the tool creates a prompt, there is then an automatic transformation of the prompt into code. Such automatic transformation is generally accepted as not to create a new work (after all, anybody else inputting the same prompt would have a reasonable expectation of generating the same output modulo some noise due to versioning and possibly other local context).
Claud code and in general AI generated code does not at present create a new work. But the prompt, that part which you input may be sufficiently creative to warrant copyright protection.
In the US, the copyright office (as the article you link to says), has declined to define “meaningful” contribution. If you want to argue that the user doesn’t own it for incredibly trivial prompts, I won’t argue (though I consider that to be non-useful code).
Every developer I’ve seen use these tools has have engaged in a meaningful contribution: specific directions across multiple prompts, often (though not always) editing the code afterwards, manually running the code and promoting for changes, etc.
Until the courts, legislators, or the copyright office define something otherwise, I’m highly confident of my assertion. (Mostly because of the insane number of hours I’ve spent with counsel on this. And, as a disclaimer, since I am biased: I worked on Copilot and Google’s various AI assisted coding products as an SVP and VP.)