Former Vice President Joseph R. Biden has shown flimsy fealty to the facts in his own political career, but his campaign is now fighting to be the arbiter of truth, lobbying media outlets to squelch stories and refuse ads he says stretch the truth.

His campaign asked networks to stop booking Trump ally Rudolph W. Giuliani and then tried to organize a boycott of a Trump campaign ad by accusing the president of lying about Mr. Biden’s actions to try to get a Ukrainian prosecutor fired.

And the Biden campaign on Thursday viciously attacked The New York Times for running an opinion column by an investigative reporter who questioned the international deal-making of Mr. Biden’s son, Hunter, while his father was vice president.

“Are you truly blind to what you got wrong in 2016?” Biden spokeswoman Kate Bedingfield demanded of the paper.

The attempt to berate the press has so far shown only modest payoff.

CNN and NBC fell in line, barring the Trump ad from its airwaves. But other major outlets refused, including Facebook.

“Our approach is grounded in Facebook’s fundamental belief in free expression, respect for the democratic process, and the belief that, in mature democracies with a free press, political speech is already arguably the most scrutinized speech there is,” said Katie Harbath, public policy director at Facebook. “Thus, when a politician speaks or makes an ad, we do not send it to third-party fact checkers.”

The line between truth and lies in politics has been getting murkier — so much so that a cottage industry of independent fact-checkers has popped up to sift through the scads of ads that are blasted into living rooms and splashed across computer and phone screens every election cycle.

But asking the press to cancel a candidate’s ads could be the beginning of a slippery slope, said Steffan W. Schmidt, political science professor at Iowa State University.

“Political ads are almost always exaggerations — my polite term for lies and fabrications,” Mr. Schmidt said. “So almost every Democratic and Trump ad would need to be rejected.”

That would also extend to social media, where candidates freely offer their opinions — sometimes unhinged from nuance or veracity.

“The problem as always is that the truth is somewhat subjective and often the untruths are embedded in other stuff so it’s hard to separate,” the professor said.

The Trump ad that offended the Biden campaign claims the then-vice president “promised Ukraine $1 billion if they fired the prosecutor investigating his son’s company.”

“But when President Trump asks Ukraine to investigate corruption, the Democrats want to impeach him,” the narrator says in the spot, which has been viewed millions of times.

Mr. Biden did once brag that he used $1 billion in U.S. loan guarantees as a cudgel to get Ukraine to force out the prosecutor.

Tim Murtaugh, a Trump campaign spokesman, says the Biden campaign is scrambling to silence them because the “truth hurts.”

“The best part is our ad includes Biden bragging about this very thing on videotape,” Mr. Murtaugh said. “On what planet does he think he can deny it’s true?”

But fact-checkers say Mr. Biden’s stance against the prosecutor was shared by other international partners who felt the prosecutor wasn’t aggressive enough and needed to go. Those fact-checkers say Mr. Biden’s threats were fair, and weren’t tied to his son.

Factcheck.org said: “The TV ad, in short, creates a false narrative about Joe Biden to discredit the impeachment inquiry, but it doesn’t have the ‘facts’ to support its claim.”

Travis N. Ridout, co-director of the Wesleyan Media Project, which tracks ads in federal elections, said that it is “fairly rare” for TV stations to “reject something because it is untruthful.”

“I think in large part that’s because federal regulations require them to not censor candidate ads,” Mr. Ridout said. “In the vast majority of instances, you do hear candidates’ complaints and they go nowhere.”

“They might threaten to sue or whatever, but the lawsuit would be against the other candidate, not necessarily the TV station,” he said.

Being the arbiter of truth is perhaps an odd fit for Mr. Biden, whose first presidential campaign flamed out in 1987 after he apologized for stealing passages from speeches by other politicians in his own addresses.

In this current campaign, he’s been chided for misrepresenting the Obama administration’s immigration policies, his stance on the Iraq War and his voting record in the Senate.

“One of Biden’s problems is that he has a record of making stuff up,” Mr. Schmidt said. “Of course, that doesn’t have to be a liability because according to most truth-checking projects, President Trump makes up a whole lotta stuff and it hasn’t hurt him so far!”

Indeed, Politifact has scored 512 of the 724 statements — or 70% — they’ve graded from Mr. Trump as “Mostly False,” “False,” and “Pants on Fire.” The group ranked 35 of the 96 claims — or 36% — they’ve graded from Mr. Biden in a similar fashion.

Patrick Griffin, a GOP strategist, said the Biden attempt to control the airwaves is patronizing to voters.

“If we can’t convince him that his policies are bad, then they say we have to figure out a way to stop him,” Mr. Griffin said. “People can’t be as sensitive and informed and as enlightened as they are.”

Hank Sheinkopf, a Democratic strategist, said the Biden campaign is wasting its time and said Mr. Trump has figured out that politics is less about fairness than about “combat.”

“The idea that you can stand there while the dragon is breathing fire on you and say it is unfair the dragon can do that is a throwback to another era,” he said. “There is no ‘fair’ in public discourse right now.”

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