A CAMBRIDGE RESIDENT was arrested Thursday morning in New York City for allegedly tweeting that he would pay $500 to anyone who killed an Immigration and Customs Enforcement agent.

Today’s Boston Herald goes all in on the story, putting it on its front-page and featuring a newspaper editorial and column by Joe Battenfeld on the story. The gist of the Herald news story, as well as a Boston Globe story that appears on the front of its Metro section: There’s a bright line between offering heated opinion opposing something like ICE practices and making threats that constitute crimes.

“There is a point in which rhetoric veers into irresponsible and sometimes criminal acts,” US Attorney Andrew Lelling said in announcing the arrest of Brandon James Ziobrowski. Lelling said the case was part of a “rising trend upwards” of threats against law enforcement officers, especially immigration officials. “Feeling strongly on this subject is fine. Putting peoples’ lives in danger, not fine,” Lelling said of the debate over immigration policy.

But the Herald editorial and Battenfeld column seem to suggest that line is actually not so bright. Indeed, the headline on the paper’s editorial on the Ziobrowski arrest doesn’t even mention the 33-year-old Cantabrigian, but instead spotlights another Cambridge resident: “Watch your words, Liz Warren,” it reads.

It quotes from Warren speeches ripping ICE policies under the Trump administration for putting “children in cages” and ripping families apart, a moment she called “a moral crisis for our country.”

“There is a moral crisis in our country, and recklessly vilifying those who protect us on the border as brutes and the entire criminal justice system as “racist” is creating it,” says the editorial. “Casting law enforcement as the bad guy is upside-down thinking and we are reaping the dark rewards,” the editorial continues, implying a connection between Warren’s rhetoric and Ziobrowski’s alleged threat against ICE agents.

Battenfeld seems to echo that sentiment, writing that “the debate over ICE has gotten out of control — and dangerous.”

“Every politician like US Sen. Elizabeth Warren needs to think carefully about what they are saying when they demonize the controversial agency, and what their words might be provoking,” he writes.

But Battenfeld seems to shoot down his own speculation. “There’s no evidence to suggest that Ziobrowski was motivated by the words of Warren and other Democrats,” he writes, “but it’s safe to say that he was supportive of the abolish-ICE movement.”

According to the Globe story, Lelling said he did not think there was a connection between calls from politicians and activists to abolish ICE and threats against agents.

Warren and others have certainly deployed heated language to criticize ICE. But decrying the administration’s practice of separating adults crossing the border illegally from their children has hardly been limited to left-leaning firebrands, with the chorus of voices condemning the policy including former first lady Laura Bush and even the wife of the man responsible for it, Melania Trump.

Of course, the question of whether overcharged rhetoric is prompting people to cross the line into criminal threats or attack is very much in the air. But it has mostly been centered on whether Trump’s rants against immigrants have played a role in inspiring an increase in hate incidents across the country or demonstrations like the white supremacist rally one year ago in Charlottesville, where, in discussing the rally and the counter-demonstration against it, Trump declared there to be “some very fine people on both sides.”