Defamation
Under New York Times v. Sullivan, a public figure suing for defamation must prove actual malice, meaning knowledge of falsity or reckless disregard for the truth. The litigation process also exposes the plaintiff to discovery and depositions, which can produce worse reputation outcomes than the original publication. Most defamation cases end in settlement.
See Litigation PR: Best Firms, Costs and Rules and the Depp v. Heard analysis.