Facebook and Twitter have rejected a request by Speaker Nancy Pelosi to remove a video posted by President Trump that was edited to make it appear as though she were ripping a copy of his State of the Union address as he honored a Tuskegee airman and other guests.

The decision highlighted the tension between critics who want social media platforms to crack down on the spread of misinformation and others who argue that political speech should be given wide latitude, even if it’s deceptive or false.

The debate has accelerated during the 2020 presidential campaign, as Democrats in Congress have demanded that Facebook and other tech companies take tougher action, while figures on the right have fought back, arguing that such policing could muzzle conservative viewpoints.

Into that highly politicized environment came the video posted by Mr. Trump to his Twitter account on Thursday.