Eric Goldman (Santa Clara University Asst Professor, School Of Law) wrote a blog post (see here) and a much longer paper (see here) on the subject of businesses trying to ban negative consumer reviews.
New York and California have laws that prohibit the enforcement of contract clauses that try to stop consumers from writing negative reviews. Apparently, that doesn’t stop judges from either not understanding the law or not caring.
A New York judge agreed to hear a case regarding a VRBO rental agreement that prohibited negative reviews. A renter was apparently unhappy and wrote a negative review. The landlord attempted to get the renter to take down the review in exchange for $300, but the renter refused and the landlord is suing him in New York court. We shall see how that turns out.
Other people have gotten very creative. Some doctors required patients to sign an agreement before they would see them that assigned the copyright for any review that they might write in the future. Then if there was a bad review, they would send the site a DMCA takedown notice as the owner of the review. Since DMCA is kind of an iron fist, web site owners typically take the reviews down. Section 230 of the U.S. Code generally protects web site owners from liability in cases of when a contributor writes a negative review, but if the reviewer no longer owns the review, then DMCA prevails.
One lawyer would sue review writers on behalf of the harmed doctor or dentist. Typically, he would get a summary judgement because the review writer would not show up in court. In cases where the review was posted anonymously, there was no way to inform the review writer about the lawsuit, so they definitely would not show up. The lawyer would then ask the judge to grant his client the copyright to the review as damages and he would then send the website a DMCA takedown notice (see article). Judges would often do this even though it is a violation of copyright law (you can only involuntarily lose your copyright in cases of bankruptcy).
The blog post has links to a number of related articles and until there is a national law, which Congress has considered (see here) but not passed, it is still a dicey subject.
In the meantime, unless you are in New York or California, the law is not on your side, especially if you agree to a contract with a negative review ban.
At least you know to look for this.