The law and legal professional ethics require of counsel a duty of candor in the practice of law. This includes a duty to not knowingly make false statements of fact, and to not offer evidence the lawyer knows to be false. These principles are considered essential to maintaining both substantive fairness for participants in the process, and trust in the integrity of the process for those outside of it.
Users of information tools in public contexts are not, of course, subject to the same duties. And publication of false information is generally protected by the First Amendment, unless it falls into one of the defined exceptions. I’m doubtful a law against publication of false information would be sustained.
It is, however, perfectly acceptable for most information technology platforms to adopt such a policy and seek to enforce it as best they can. That is, platforms could create and enforce rules against publication of information known to be false. A recent publication from the NYU Stern Center for Business and Human Rights contends platforms should do so. This post concurs: subject to some limitations, private platforms can and should take a position that use of their services to intentionally or carelessly spread false information violates terms of service. Read more about Tool Without A Handle: A Duty of Candor