Not really. How do you imagine this could work if it was true? It's a great excuse if you're looking to throw your weight around of course. Oh the poor Disney corporation had to sue that primary school for a bajillion dollars, or else they would lose their trademark. Does that sort of thing even pass the sniff test for you?
And it works out great for lawyers too. Instead of only getting paid when there's actual controversy that needs their skills, they can collect a fee for this "protection" work.