The decision by the Democratic National Committee to forgo a presidential primary debate on Fox News Channel had expected reactions from many corners. Democrats, frustrated by the network’s coverage and the New Yorker’s recent look at its internal machinations, seemed largely pleased. Fox News, on the other hand, wasn’t.

On Tuesday morning, Axios reported that the network was still trying to twist arms to get a Democratic debate. It quoted host Bret Baier: “We have viewers that are Democrats, independents, Republicans — and there are lots of them.”

That’s obviously true. Fox News is a popular network and, despite the frequently sympathetic coverage of President Trump that dominates its opinion shows, it’s not as though there aren’t Democrats and independents who support the president. It’s just worth asking how broadly Baier is overstating his case. After all, you could probably find a vegetarian at a hot-dog-eating contest, but it might not be a great place to go to reach out to vegetarians specifically.

Getting data on the partisan composition of news networks’ audiences is trickier than it may seem. We frequently cite polling from Suffolk University that asks people specifically which news or opinion source they trust the most. Their most recent survey, completed in December, shows Fox News with both more respondents citing it as a preferred source and about two-thirds of those respondents identifying as Republican.

The audience for both CNN and MSNBC is mostly Democratic — but that’s in part because Fox News gobbles up so much of the Republican pool of viewers.

Pew Research Center put this into a different context in early 2017. Fox News was by far the most commonly cited source for 2016 campaign coverage among Trump voters. For Hillary Clinton voters, CNN was the most common.

Notice, though, that even 3 percent of Clinton voters identified Fox News as their primary source of news. For every six Clinton supporters who cited CNN, one pointed to Fox.

According to another Pew poll released in 2017, 10 percent of Fox News’s audience identifies as liberal Democrats. That’s far less than the percentage that identifies as conservative Republicans, but again, it’s not nothing. In fact, more than half of Fox News’s audience isn’t made up of conservative Republicans (and conservative independents who lean Republican).

The Washington Post’s audience, Pew determined, skewed more heavily liberal than CNN or MSNBC.

Speaking of The Post, we also polled on media preferences late last year. We asked people to identify their most trusted sources of political news, including news outlets, companies and people. Among those who identified any of the cable news networks as their first or second most-trusted sources, about half of those picking Fox News were Republican. About a fifth were Democrats.

The density of Democrats among those who picked CNN or MSNBC as their first or second choices was about the same as the density of Republicans among those citing Fox News. Independents made up about the same portion of the viewership of each network.

In other words, Baier is not wrong.

That said, the Democratic Party will obviously be reaching a greater percentage of Democrats by airing on one of the other cable networks. But given Fox News’s consistent lead in overall audience, the actual number of extra Democrats reached by airing on CNN as opposed to Fox News is probably smaller than you might expect.

None of this is really what the DNC’s decision was about. It was meant to send a message to the network that its coverage of and approach to the Trump administration weren’t acceptable — and it was meant to take a position in the cultural fight over that approach.

When I was in high school, I interned briefly for my local congressman at the time, Rep. Jim Traficant (D-Ohio). In the main district office, Rush Limbaugh was piped over the speaker system all day, every day. Traficant’s politics may not have always aligned with Limbaugh’s — but he still listened.

Emily Guskin contributed to this report.