Park City, Utah (CNN) Donald Trump's recent remarks that he could "shoot somebody" and not lose political support was an "insult" to communities struck by gun violence, according to the director of a powerful new documentary about the mass school shooting in Newtown, Connecticut.

"It speaks to the insensitivity and the desensitization" surrounding the issue, Kim Snyder, whose film "Newtown" debuted here at the Sundance Film Festival, told CNN on Monday.

"Spending three years in and around Newtown with survivors in that community, you really do start to really understand the insult," she continued, "and what it feels like when people are so cavalier in speaking about gun violence in such an insensitive and cavalier way."

At a rally in Sioux City, Iowa, on Saturday, Trump said, "I could stand in the middle of Fifth Avenue and shoot somebody and I wouldn't lose voters." Trump initially declined to respond to questions about what he said, but told CNN's Wolf Blitzer on Monday he was "joking."

Hours after Trump made his initial comment, Snyder and "Newtown" producer Maria Cuomo Cole dined with former Congresswoman Gabby Giffords and her husband, Mark Kelly. (Cuomo Cole is the sister of CNN "New Day" co-host Chris Cuomo.)

Giffords and Kelly were vocal about their disgust at what Trump said during the rally, Snyder and Cuomo Cole said. Gabby Giffords survived a gunshot wound to the head during a constituent event in Tucson, Arizona, in 2011 and now works with her husband to promote gun safety legislation.

The Trump campaign didn't immediately respond to a request for comment from CNN.

For Snyder, who arrived in Newtown six weeks after a 20-year-old gunman, Adam Lanza, had fatally wounded 20 first graders, six educators, and his mother on December 14, 2012, before turning one of his weapons on himself, the political nature of the film is inescapable.

"You can't talk about Newtown," she said, "without talking about the conversation of guns and gun reform in the country."

The documentary, which debuted here on Sunday, weaves elements of that fight into the more deeply felt personal accounts provided by the parents of three of the youngest victims.

They come together in a searing April 2013 scene, following the Senate's failure to agree on a compromise amendment that would have required background checks on all commercial gun sales. It is a particular blow for Mark Barden, whose son Daniel was among the youngest victims.

The vote, Snyder says, was "incredibly demoralizing and incredibly disappointing" to people like Barden, Nicole Hockley and David Wheeler.

All three lost sons and their struggle, both to advance gun safety law and manage their overwhelming grief, creates a gut-punch of a film.

"I have this need to know what he experienced," Barden says in "Newtown," explaining the dizzying grief that colors his days. He asks parents to contemplate trying "to interpret what your 7-year-old experienced as he's being murdered in his first-grade classroom."

"We're all terrified of forgetting what he looked like or sounded like," Wheeler confesses, speaking about his son Ben.

Like many of the parents interviewed, Wheeler's thoughts drift toward the lonely hours, and "the tiny, minor questions that become huge questions when you can't sleep at night." That, he says, is what drives his activism.

But the film relies as much on silence, and what its subjects withhold or cannot yet bear to consider, as the details they choose to share.

A doctor on duty at a local hospital at the time of the shootings describes in detail what a bullet from an AR-15 rifle, the weapon used by Lanza, does to the body of a six- or seven-year-old child. But he does not speak about the one victim who made it to the emergency room before succumbing.

Two emergency responders begin to explain what they found at the scene, only to pull back.

State Police Sgt. William Cario was the first to enter, but he too demurs.

"I don't think anyone needs to know specifically what we saw," he says.