The situation is similar with image generation. An artist can draw a picture of Mickey Mouse without any issue. But if you pay an artist to draw you the same picture, that would also be a violation.
With generative tools, the users are not themselves writers or artists using tools - they are effectively commissioners, commissioning custom artwork from an LLM and paying the operator.
If someone built a machine that you put a quartner in, cranked a handle, and then printed out pictures of the Disney character you choose, then Disney is right in demanding them to stop (or more likely, force a license deal). Whatever technology drives the machine, whether an AI model or an image database or a mechanical turk, is largely immaterial.