(CNN) Almost as soon as the bombs arrived in the mail, the debate began: What role does violent political rhetoric have on these real-life acts of violence?

Well, truth be told, a version of this debate has been raging for a while. Witness the reactions to President Trump's recent praise of a congressman for body-slamming a reporter.

But the debate has been renewed now, in the wake of the threatening deliveries to CNN's New York office and several prominent Democratic politicians on Wednesday. The intended recipients all had something in common: They were frequent targets of right-wing criticism.

Or as the Washington Post succinctly put it: "Amid incendiary rhetoric, targets of Trump's words become targets of bombs."

At a rally in Wisconsin on Wednesday night, Trump paired his remarks decrying political violence with fresh criticism of the media.

"The media also has a responsibility to set a civil tone and to stop the endless hostility and constant negative and oftentimes false attacks and stories. Have to do it," he said.

Speaking on CNN, senior political analyst David Gergen said that Trump "hasn't taken an ounce of responsibility or accountability" for his own rhetoric.

"Trump unleashed the dogs of hatred in this country from the day he declared he was running for president, and they've been snarling and barking at each other ever since," Gergen said. "It's just inevitable there are going to be acts of violence that grow out of that."

News industry executives have repeatedly warned that Trump's reckless attacks against the media are having real-world consequences. Some journalists now travel to Trump rallies with security personnel, for example.

In a statement on Wednesday afternoon, CNN Worldwide president Jeff Zucker spoke out about the problem.

"There is a total and complete lack of understanding at the White House about the seriousness of their continued attacks on the media," he said. "The President, and especially the White House Press Secretary, should understand their words matter. Thus far, they have shown no comprehension of that."

Journalism advocacy groups uphold this view as well. Dan Shelley, the head of Radio Television Digital News Association, pointed out the irony in Trump's recent statements.

On Wednesday, responding to the mailings, Trump said "threats of political violence of any kind have no place in the United States of America."

But, Shelley said, "those words were uttered by the same person who has used harsh rhetoric targeting journalists and political opponents during campaign rallies in an extremely tense and divisive political environment."

Shelley repeated a line he has used recently: "Don't succumb to intimidation and fear," he said to fellow journalists. "Watch your backs, but don't back down."

As reports of suspicious packages piled up on Wednesday, many commentators and political observers urged caution and lamented the rush to judgment that many others were making.

Partisans on the left and the right traded barbs, particularly on social media, where the hashtag #MAGABomber was the top trending topic on Twitter in the US. The hashtag's assertion was that the perpetrator supported Trump's "MAGA," or Make America Great Again, message.

Some prominent Trump supporters and far-right online personalities fought back by suggesting, without evidence, that the bombs were sent by a Democratic operative as part of a supposed "false flag" operation. This term refers to crimes committed by one party that are disguised to give the impression that they are committed by another group.

Rush Limbaugh, the conservative talk radio host who reaches millions of listeners each week, said on his Wednesday show that "it doesn't make any sense for a Republican or conservative to do this."

"But flip that! Flip that around. Would it make a lot of sense for a Democrat operative or Democrat-inculcated lunatic to do it?" Limbaugh asked, suggesting to his audience that it would because he argued the Democrats are worried they were ceding ground in the looming midterm elections.

Ann Coulter, the best-selling conservative author, wrote on Twitter that "bombs are a liberal tactic."

And Candace Owens, the communications director for Turning Points USA, a conservative organization with close ties to the Trump family, wrote in a now-deleted tweet that "the only thing 'suspicious' about these packages, is their timing."

"Caravans, fake bomb threats -- these leftists are going ALL OUT for midterms," Owens added.

The incendiary comments about the bomb incidents were not limited to Limbaugh, Coulter, and Owens. To the contrary, the spreading of conspiracy theories was a common theme among individuals on the fringes of the right.

The "false flag" claims were condemned by numerous commentators on cable news.

Numerous news organizations rallied to support CNN.

On Fox News, "Special Report" anchor Bret Baier ended his hour by saying "days like today remind us of the danger that does exist, and has been condemned from all sides. Our thoughts today were with our colleagues at CNN as they were dealing with this real time, and we're very happy everybody's okay."

And Fox News head of human resources Kevin Lord issued an internal memo in which he expressed support for CNN.

"We condemn all attempted acts of violence against media organizations and our thoughts are with CNN for the safety of all of their employees," Lord said in the memo, a copy of which was obtained by The Hollywood Reporter.