The point of the "no legal threats" policy is that legal threats end discussion. Once lawyers and courts are involved, discussion is over and you're on to adjudication. In other words, when someone is actually carrying out legal action, talking about it on Wikipedia is pointless- which means that legal threats have absolutely no value for any kind of rational discussion.
So, as you are asking, how should someone enforce their legal rights? Answer: By pointing out their legal rights, without making threats. "This item is my intellectual property and you do not have permission to use it." At that point, we should remove it immediately. There is no need to mention, or benefit from mentioning, lawyers or lawsuits.
I don't think we should penalize copyright holders for serving WP with a cease-and-desist for a copyvio, whether formally or informally, although we might want to require them to, as a prerequisite for their future participation, state that their grievances are met and that no further action will be taken.