Did Joe Biden endorse President Trump at a recent campaign event? “We can only re-elect Donald Trump, ” he said. But everyone understood that Mr. Biden either mixed up his words or was making an entirely different point.

Everyone but the people who run Twitter . The social-media platform recently rolled out a new policy aimed at “manipulated media.” Its first target: a 13-second clip tweeted by Dan Scavino, White House director of social media, featuring Mr. Biden’s words. The Biden campaign quickly denounced the video as “disinformation” and pressured both Twitter and Facebook to take it down. Twitter slapped the manipulated-media label on it. Facebook put a “partly false” screen over it. The debate that followed helped earn the clip millions of views.

Something similar happened when Mike Bloomberg’s campaign tweeted a humorous video that inserted the sound of crickets chirping after he landed a one-liner during a debate. Former Obama staffer Ben Rhodes called it “pure disinformation.” The Washington Post “fact checker” awarded it “four Pinocchios.” Imagine going after President Lyndon B. Johnson’s 1964 “Daisy Girl” ad because viewers might think the child actually died in a nuclear strike.

Today’s media and political gatekeepers aren’t concerned that people will find these clips misleading; they are rightly concerned that they will be effective. Political satire works because it challenges those in power while using humor to draw people into the discussion. Internet speech, viral videos and memes threaten those seeking to control the political narrative. By bypassing self-appointed gatekeepers, an outsider can now carry a message directly to the public. The media must often play catch-up—covering the messages and story lines that are already resonating with people.

This explains efforts to equate political speech with the entirely separate categories of doctored deep fakes, illegal content and deceptive cheap fakes. These attempts to curtail lawful political speech confuse the public, making it harder to identify and build consensus around media that has truly been doctored or manipulated. Many of the latter sort of videos are on their way—whether aimed at influencing elections or otherwise swaying public debate.