[Terr_]

I don't think so: The user is merely making a request for copyrighted material, which is not itself infringing, even if their request was extremely specific and their intent was obvious.

OpenAI would be the company actually committing the infringement and providing the copy in order to satisfy the request.

If the law suddenly worked the other way around, companies would no longer be able to prosecute people for hosting pirated content online, because the responsibility would lie with the users choosing to initiate the download.