Need I remind you that companies are using the exact same "reasoning" to shut down (negative) reviews, caricarture, persiflage and what not... even though we have fair use to technically protect that.
Do you have examples of this case? I would be surprised if caricatures are allowed to be taken down by the court, as that should falls under fair use. Perhaps the author of the caricature decides to take it down anyway rather than take it to court which could be expensive for both parties.
Copyright owners can contact you about it, write a cease and desist letter or whatever they think can scare you off. Nothing restricts them from doing this. What you decide between you two is up to you. If you can't come up with an agreement, then you have the court which shall decide what happens. But if you decide to take it down before taking it to court, then case is settled. However, it's not that it's illegal to draw caricatures, it's just you prefer to take it down rather than going to through the costly legal battle in court, which benefit nobody except the lawyers.
No, it's never been legal to create any derivative works unless there's an agreement for it, which I shall advice the OP to do if he's truly passionate about it. You can always publish your work without permissions, nothing is stopping you from doing that. Just don't be surprised if you receive a C&D or taken to court.