The issue is not whether Facebook, as a private company, can filter whatever it likes, but whether it does so reliably and truthfully in a way its users can trust.
Facebook can indeed decide what to filter, but its also permissible for other organizations to make users aware that Facebook may filter and display misleading messages based on inaccurate fact checking and that the fact-checking organization that caused the filtering defamed a reputable publication by falsely alleging that their content is a hoax.
Facebook can indeed decide what to filter, but its also permissible for other organizations to make users aware that Facebook may filter and display misleading messages based on inaccurate fact checking and that the fact-checking organization that caused the filtering defamed a reputable publication by falsely alleging that their content is a hoax.