By that he meant he wanted to address the inability or refusal of Mr. Trump, his followers and his administration to separate the real from the fake. And so Mr. Oliver took up four Trump-related questions: How did a man with such a contempt for or poor grasp of the truth end up as president? Where are his lies coming from? Why do so many people believe them? And what can be done about it?

The first three have been thoroughly picked over by all sorts of journalistic outlets, including some conservative ones, and two-thirds of the way into Sunday night’s show it seemed as if Mr. Oliver had nothing new to add. He and his former “Daily Show” colleague Samantha Bee, on her TBS show “Full Frontal,” have taken some of the deepest dives into the surreality of the Trump ascendance, so it would have been disappointing if Sunday’s episode had simply revisited problems that have been exhaustively documented elsewhere.

But of course Mr. Oliver had something else up his sleeve. “Last Week Tonight” has in its first three seasons built a reputation for quirky advocacy, whether calling for letter-writing campaigns or — as in his last show of 2016, after the election — urging viewers to give money to threatened social causes and to support news organizations financially.

Mr. Oliver kept that tradition rolling at the end of Sunday’s segment when, after establishing that Mr. Trump seems to get much of his dubious information by watching morning cable news shows, he announced that “Last Week Tonight” would be buying advertising on those shows in the Washington area. The ads, he said, would seek to impart facts that Mr. Trump has shown he does not grasp or believe. Samples included spots featuring a folksy cowboy, which were designed to resemble catheter ads but instead related facts about the nuclear triad, the demographics of urban areas and more. The first such ad will run Monday on several outlets, Mr. Oliver said.