That is more or less the case, in that the online owners cannot be sued for what the users post. However, that does not prevent the site from censoring what users post if you take the time to read the law. 

Prior to federal legislation the first case was someone suing Compuserve over a post by a user. Back in the 80s. Court ruled Compuserve was a common carrier so long as it did not edit or control what was posted. 

The later legislation still absolved the site owners but also allowed editorial control of what users posted. Without such legislation there would be millions of people suing Facebook  

At this point the online business can’t be truly a common carrier, at least in the sense of a telephone company. 

Cubby, Inc. v. CompuServe Inc., 776 F. Supp. 135 (S.D.N.Y. 1991)<sup id="cite_ref-Cubby_1-0" class="reference">[1] was a 1991 court decision in the United States District Court for the Southern District of New York which held that Internet service providers were subject to traditional defamation law for their hosted content.<sup id="cite_ref-Cubby_1-1" class="reference">[1] The case resolved a claim of libel against CompuServe, an Internet service provider that hosted allegedly defamatory content in one of its forums. The case established a precedent for Internet service provider liability by applying defamation law, originally intended for hard copies of written works, to the Internet medium. The court held that although CompuServe did host defamatory content on its forums, CompuServe was merely a distributor, rather than a publisher, of the content. As a distributor, CompuServe could only be held liable for defamation if it knew, or had reason to know, of the defamatory nature of the content.<sup id="cite_ref-section581_2-0" class="reference">[2] As CompuServe had made no effort to review the large volume of content on its forums, it could not be held liable for the defamatory content.