Saying something and printing a trademark are two different things. You have the right to say anything you want. And there is a lot of laws that regulates what you can say. But if a company pays for a trademark, they are paying for the rights for it. another company can not use it for their business. Whenever a real business deals with this, they have to get permission or pay to use it. Like a sports magazine gets permission to print their logo on a section. If a company uses a trademarked logo without permission they will lose in court every time. It is the same as stealing.
As for free speech... people can say what they want, but they can't say lies about people. that is called slander and it is a crime. Tabloids get away with it by having a good law firm (they get sued all the time and lose) and having sources that can "confirm," and they word their stories so that it is in the grey area. Like instead of calling someone a killer, they say "did she kill them?" with a question that implies what they mean. that is why you see so many question marks on the front of tabloids. but yeah, it has nothing to do with what is being discussed. This issue has nothing to do with the site getting shut down.