Some of the unflattering private messages among the network’s hosts and executives may never become evidence when Dominion Voting Systems’ defamation case against Fox News goes to trial.For the past three weeks, a drip, drip, drip of disclosures have exposed widespread alarm and disbelief inside Fox News in the days after the 2020 presidential election, as the network became a platform for some of the most insidious lies about widespread voter fraud. These revelations are the most damning to rattle the Murdoch media empire since the phone hacking scandal in Britain more than a decade ago.The headlines have been attention-grabbing. Tucker Carlson, a professed champion of former President Donald J. Trump’s populist message, was caught insulting Mr. Trump — “I hate him passionately,” he wrote in a text. Laura Ingraham and Sean Hannity disparaged colleagues in their network’s news division. And Rupert Murdoch said he longed for the day when Mr. Trump would be irrelevant.These examples and many more — revealed in personal emails, text messages and testimony made public as part of Dominion Voting Systems’ $1.6 billion defamation lawsuit against Fox News — are embarrassing. But whether they pose serious legal jeopardy for Fox in that case is far less clear.The messages that led to some of the biggest headlines may never be introduced as evidence when the case goes to trial next month, according to lawyers and legal scholars, including several who are directly involved in the case. Fox is expected to ask a judge to exclude certain texts and emails on the grounds they are not relevant.Laura Ingraham disparaged Fox News colleagues in private messages released recently.Rebecca Noble for The New York TimesBut the most powerful legal defense Fox has is the First Amendment, which allows news organizations broad leeway to cover topics and statements made by elected officials. In court, Fox’s lawyers have argued that the network was merely reporting on what Mr. Trump and his allies were saying about fraud and Dominion machines — not endorsing those falsehoods.Media law experts said that if a jury found that to be true — not a far-fetched outcome, they said, especially if lawyers for the network can show that its hosts did not present the allegations as fact — then Fox could win.Fox News v. Dominion Voter SystemsDocuments from a lawsuit filed by the voting machine maker Dominion against Fox News have shed light on the debate inside the network over false claims related to the 2020 election.Running Fox: Emails that lawyers for Dominion have used to build their defamation case give a peek into how Rupert Murdoch shapes coverage at his news organizations.Behind the Curtain: Texts and emails released as part of the lawsuit show how Fox employees privately mocked election fraud claims made by former President Donald J. Trump, even as the network amplified them to appease viewers.Tucker Carlson’s Private Contempt: The Fox host’s private comments, revealed in court documents, contrast sharply with his support of Mr. Trump on his show.A Show of Support: In his first public remarks since the recent revelations on Fox News, Mr. Murdoch’s son Lachlan, the chief executive of the Fox Corporation, issued a full-throated show of support for Suzanne Scott, who is at the helm of Fox News Media.“I think the case really will come down to a jury deciding whether the company or the commentators did or didn’t endorse — that really is the key question,” said George Freeman, a former New York Times lawyer who is now executive director of the Media Law Resource Center, which assists news organizations with legal issues.“It gives Fox, I think, a fighting chance,” he added.Despite the ways Fox could prevail with a jury, legal scholars say Dominion’s case is exceptionally strong.Lawyers for Dominion argue that the claims made by Fox’s hosts and guests about its machines and their supposed role in a nonexistent conspiracy to steal votes from Mr. Trump was anything but dispassionate, neutral reporting.“Truth and shared facts form the foundation of a free society — even more so here,” its lawyers said in a brief, filed with the court on Thursday. “The false idea that Dominion rigged the 2020 presidential election undermines the core of democracy.”It is rare for First Amendment lawyers to side against a media company. But many of them have done just that, arguing that a finding against Fox will send an important message: The law does not protect those who peddle disinformation. And it would help dispel the idea, First Amendment experts said, that libel laws should be rewritten to make it easier to win defamation suits, as Mr. Trump and other conservatives, including Justice Clarence Thomas, have suggested.In its most recent filings, Dominion argued that the law was more than adequate to find Fox liable.“If this case does not qualify as defamation, then defamation has lost all meaning,” Dominion argued in a legal filing made public on Thursday.But legal experts said that the case would rise or fall not based on how a jury considered lofty concerns about the health of American democracy. Rather, they said, Dominion’s challenge will be to persuasively argue something far more specific: that Fox News either knowingly broadcast false information or was so reckless that it overlooked obvious evidence pointing to the falsity of the conspiracy theories about Dominion.Though the coverage of the case has largely focused on the disparaging comments the network’s star hosts and top executives made in private — about Mr. Trump, his lawyers and one another — those remarks could only help Dominion’s case if they pointed to a deeper rot inside Fox, namely that it cynically elevated false stories about Dominion machines because its ratings were suffering.The one episode of Mr. Carlson’s show that Dominion cited as defamatory included an interview with Mike Lindell, the MyPillow chief executive.Fox News“When I see the headlines that are primarily about Tucker Carlson or Sean Hannity, those are conversations that the litigation was designed to spur,” said RonNell Andersen Jones, a First Amendment scholar and law professor at the University of Utah.“At least some of that evidence is going to be important atmospherically,” Ms. Andersen Jones added. But what will be more important to the outcome of the case, she said, is “what drove the narrower decisions at the individual shows.”Fox’s lawyers could ask the judge, for instance, to keep the jury from seeing most of Mr. Murdoch’s deposition on the grounds that he was the chairman of the company and played no direct role in decision-making at the show level. However, during his deposition, Mr. Murdoch did concede a key point of Dominion’s. He acknowledged that some Fox hosts had endorsed false claims of malfeasance during the election. And when Dominion’s lawyer, Justin Nelson, presented Mr. Murdoch with examples of how Fox went beyond merely providing a platform for election deniers, the Fox chairman agreed. “I think you’ve shown me some material in support of that,” Mr. Murdoch testified.Fox also plans to argue that the network’s coverage of the aftermath of the 2020 election needs to be considered as a whole, including the hosts and guests who insisted that there was no evidence of widespread fraud.And the more Fox lawyers can show instances in the coverage where its hosts rebutted or framed the allegations as unproven, the stronger their case will be.A lawyer working on Fox’s defense, Erin Murphy, said Dominion did not “want to talk about the shows where there was a lot of commentary coming from different perspectives.”Especially when those shows were ones “that had higher viewership and were the more mainstream,” Ms. Murphy added.Dominion would be on the strongest legal footing, defamation experts said, whenever it could point to specific examples when individual Fox employees responsible for a program had admitted the fraud claims were bogus or overlooked evidence that those claims — and the people making them — were unreliable.Dominion cites only a single episode each from Mr. Carlson and Mr. Hannity as defamatory: Mr. Carlson’s interview of Mike Lindell, the MyPillow chief executive, on Jan. 26, 2021, and Mr. Hannity’s interview of Sidney Powell, a lawyer who made some of the most outrageous fraud allegations, on Nov. 30, 2020.Dominion’s defamation claims against three far more obscure shows with much lower ratings are more substantial and extensively documented: “Sunday Morning Futures With Maria Bartiromo” and the now-canceled “Lou Dobbs Tonight,” both of which ran on Fox Business in 2020; and “Justice With Judge Jeanine,” which was Jeanine Pirro’s Saturday evening talk show on Fox News before the network canceled it and promoted Ms. Pirro to a regular slot on “The Five,” a weekday round-table talk show.Some of the most damning evidence to emerge involves Maria Bartiromo, legal experts say.Roy Rochlin/Getty ImagesEspecially damaging, legal experts said, is the evidence against Ms. Bartiromo. Dominion has accused her of recklessly disregarding evidence that a key source for Ms. Powell, who appeared several times on Ms. Bartiromo’s show, was mentally unstable — a “wackadoodle” by the source’s own admission.In an email, the full text of which was released last Tuesday along with thousands of pages of depositions and private messages of Fox employees, is from someone who claims to be a technology analyst named Marlene Bourne. Ms. Powell forwarded Ms. Bourne’s email to Ms. Bartiromo on the evening of Nov. 7, and Ms. Bartiromo forwarded it to her producer.In the email, Ms. Bourne describes numerous conspirators in a plot to discredit Mr. Trump, including some who had been dead for years like Roger Ailes, the former chief executive of Fox News. She writes that she is capable of “time-travel in a semiconscious state” and that when she is awake she can “see what others don’t see, and hear what others don’t hear.” She also says she has been decapitated and that “it appears that I was shot in the back” once after giving the F.B.I. a tip.“If we’re really zeroing in on where the strongest evidence is,” Ms. Andersen Jones said, “it’s the wackadoodle email. Because the real question is whether you had subjective awareness of the likely falsity of the thing you were platforming on your show.” More