How should online search engine operators deal with requests for removal of links to (allegedly) inaccurate or fake third-party content?

Online search engine operators (‘search engines’) are often faced with individuals (applicants) requesting that an online negative publication or review about them no longer be indexed (linked) in the engine operator’s search results. In doing so, it is often argued that that negative publication or review would contain inaccurate or false information. For example, a