https://www.federalregister.gov/documents/2023/03/16/2023-05...
So I think the law, at least as currently interpreted, does care about the process.
Though maybe you meant as to whether a new work infringes existing copyright? As this guidance is clearly about new copyright.
Who created the work, it's the user who instructed the AI (it's a tool), you can't attribute it to the AI. It would be the equivalent of Photoshop being attributed as co-author on your work.