No, this isn’t really correct. The US Copyright Office has released policy that pretty clearly states where the line falls and it’s certainly beyond super simple prompts. In fact, by the reasoning in the policy document, I’d say it’s any time where if the AI were replaced with a human and you’d want a work for hire agreement to assign copyright, then that is likely non-copyrightable subject matter.
I’ll add, how this works with modern AI art flows, still remains to be seen, but I think probably on the side of no copyright. Currently, works use very elaborate prompts, some edits, bashes, and masks in an editor and then img2img and inpainting to really get your work where it needs to be. However, under the current rubric, the sort of nexus of creativity is still happening in the model so unlikely to be granted copyright.