That’s not correct. The issue is not whether you play it off as your own, but how much the damages are that you can be sued for. If you recite something that you memorized in front of a handful of friends, the damages are non-existant and hence there is no point in sueing you.
But if you give a large commercial concert and perform a cover song without permission, you will get sued, no matter if you say “This song is from <insert original artist> and not from me”, because it’s not about giving credit, it’s about money.
And regarding getting something published: This is not so much about big name art like Harry Potter, but more about people doing smaller work. For example, voice actors (both for movie translations and smaller things like announcements in public transport) are now routinely replaced by AI that was trained on their own voices without their permission.
Similar story with e.g. people who write texts for homepages and ad material. Stuff like that. And that has real-world consequences already now.