Background: I think my dd1 could be diagnosed with an anxiety disorder if we chose to go that route, but we've not so far.
In the radio situation I probably would have put the suggestion of a movie or something in her head, but I would have turned it into a question so I wasn't really lying.
DD1 (fearfully): "Mommy, what was that man saying about a 'school shooting' and a 'gunman?'"
Me: "I'm not sure." (I'm not. I changed the station and didn't hear the whole thing, so that's true.) "Do you think maybe he was talking about a movie or something? It didn't sound like anything we wanted to listen to. Would you like to hear some music instead?"
We so just don't go too many scary places with dd1, but I try not to flat out lie either. It's just like the Santa Claus thing. We don't play it up, but if they wanna play the game I'm happy to play along. If they ask if it's true, I turn it around and ask them what they think. dd1 sometimes says that mommy and daddy put stuff in the stockings, but sometimes she says that Santa is real. She doesn't really wanna know for flat out sure yet. She's actually more interested in pretending along this year than when she was little. She was very fearful of a strange looking man coming into her house in the middle of the night as a tot.
Back to the scary things like war and violent death and murder and rape and other atrocities, I do acknowledge that people can be very mean to each other sometimes, but I don't go into details about that kinda stuff. I approach it like sex ed and give little bit of info, but wait for them to ask more questions as needed. (Although, they really know quite a bit about sex). I think a lot of the news is practically R-rated in terms of violence and I definitely have some G-rated kids in terms of sensitivity.
That dialogue sounds a bit like I would brush it off and I wouldn't, but I would be happy to plant seeds of an alternative ending besides blood and gore. Maybe somebody took a gun to school and shot out windows, but didn't hurt anybody. Maybe it was a movie. Maybe it was a toy gun. I could think up a lot of nicer alternatives than a gunman killed a buncha people. My kid needs to know that there are people who might hurt other people out there, and she should listen to her mom and her instincts and stay away from folks she doesn't feel good about, but she doesn't need to know all the R-rated details of what one human being can do to another.