When Donald Trump was seen by many in the media as a side-show with no real chance of becoming president, his behavior on Twitter twtr was an amusing distraction. But now that he is on his way to the White House, figuring out how to handle that behavior has become a critical challenge.

A classic example of this occurred on Sunday night, when the President-elect unleashed a tweet-storm about how he won the election in spite of “millions of people who voted illegally.” As with most Trump tweets, these were re-shared thousands of times within minutes.

The immediate problem posed by these tweets is that there is absolutely no evidence that large numbers of illegal votes were cast, let alone millions of them. It’s a classic conspiracy theory promoted by fake news and propaganda sites like InfoWars. Election-monitoring experts have said they have found no sign of any organized illegal voting whatsoever.

So what do media organizations do? You could argue—as many have—that news outlets have a duty to report on Trump’s comments because he is the President-elect of the United States, and he is alleging voter fraud on a fairly massive scale (despite the fact that he won).

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And this is exactly what a number of media companies did. But in doing so, some also arguably perpetuated Trump’s lie, without immediately calling it out as untrue.

CBS News, for example, tweeted the claim verbatim, simply putting “millions” in quotation marks. Several hours later, it updated the tweet to say that there was no evidence of this being true, but by then many argued that it was too late—they had already given credence to the story. The Washington Post also did this, both in a tweet and on its website.

The Wall Street Journal went a step further and put the claim in a print headline. The paper published an early version with a front-page headline that read, “Trump Takes Aim at ‘Millions’ of Votes,” with no mention of whether the claim was accurate or not. This appeared to be updated in later versions of the newspaper, where the story ran on an inside page.

At one point, a number of prominent journalists were congratulating People magazine of all places (which, like Fortune, is owned by Time Inc.) for having an accurate take on the tweet-storm, when compared to more traditional news organizations like CBS News and the Journal.

One of the problems that a live-tweeting President presents for the media is the speed with which news outlets have to move now—it’s not enough to wait and write something the following day. A tweet-storm about such an important topic is clearly a story right now, and has to be covered. And the easiest way to do that is to simply say “The President-elect says this.”

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But taking this approach avoids the challenge of presenting such comments as truthful or not, which is arguably what the media should be for. Similar challenges arose during the campaign, when cable news outlets like CNN were challenged to state outright whether something was false at the moment the candidate was speaking, not hours later.

Just as they did with debate moderation, there are those journalists who argue that live fact-checking is not something the media should do. Media columnist Michael Wolff argued in a recent interview that journalists should be “stenographers,” in the sense that they should simply report what powerful people say and leave it at that.

The problem is that this approach makes it easier for demagogues and anyone who is unconcerned with the actual truth of a statement—a group that Donald Trump demonstrably falls into—to peddle rumors and innuendo in order to advance their view of the world.

There is a broader question, of course, which is whether this kind of fact-checking actually convinces anyone. Donald Trump lied repeatedly during the campaign, and this was documented in great detail by reporters like David Farenthold at the Washington Post and Daniel Dale at the Toronto Star. And yet, millions of people chose to vote for him anyway.

Despite that, however, if the media is to have any principles at all, it has to call out falsehoods wherever they appear—especially if they come from the President of the United States—and to do so regardless of whether they believe that it is going to affect the way anyone actually thinks about him. To do otherwise would be to allow fake news and propaganda to win.