The coverage became so distorted that it prompted a reporter for Breitbart News who covers border migration, Brandon Darby, to push back. “I’m seeing a lot of right media cover this as ‘people coming illegally’ or as ‘illegal aliens.’ That is incorrect,” he wrote on Twitter. “They are coming to a port of entry and requesting refugee status. That is legal.”

In an interview, Mr. Darby said it was regrettable that the relatively routine occurrence of migrant caravans — which organizers rely on as a safety-in-numbers precaution against the violence that can happen along the trek — was being politicized. “The caravan isn’t something that’s a unique event,” he said. “And I think people are looking at it wrong. If you’re upset at the situation, it’s easier to be mad at the migrant than it is to be mad at the political leaders on both sides who won’t change the laws.”

As tends to be the case in these stories, the humanitarian aspects get glossed over as migrants are collapsed into one maligned category: hostile foreign invaders.

In November, Mr. Trump touched off an international furor when he posted a series of videos on Twitter that purported to show the effects of mass Muslim migration in Europe. Initially circulated by a fringe ultranationalist in Britain who has railed against Islam, the videos included titles like “Muslim migrant beats up Dutch boy on crutches!” “Muslim Destroys a Statue of Virgin Mary!” and “Islamist mob pushes teenage boy off roof and beats him to death!”

The assailant in one video the president shared, however, was not a “Muslim migrant.” And the other two videos depicted four-year-old events with no explanation.

These items tend to metastasize irrespective of the facts, but contain powerful visual elements to which Mr. Trump is known to viscerally respond.

Last February, Mr. Trump insinuated that some kind of terror-related episode involving Muslim immigrants had taken place in Sweden. “Who would believe this? Sweden,” he said at a rally in Florida, leaving Swedes and Americans baffled because nothing out of the ordinary had happened at all. “They took in large numbers. They’re having problems like they never thought possible.”