I'm not the person who commented earlier, but I think they were referring specifically to "mass shootings," which are more associated (at least, the perspective is) with being somewhat random. I think most Americans are more afraid of being shot at random in a mass shooting by mistake, as it would be out of their control.

Separately, gun violence as a whole is a huge problem. It is typically more associated with gang and criminal activity (which are of course big problems), but many Americans feel if you avoid dangerous areas you should more or less avoid gun violence, as the mass shootings tend to (but don't always) get an incredible amount of news coverage. Additionally, many of those mass shootings are gang shootings. It's really the school shootings, mall shootings church shootings, etc that people are afraid of. And those are a real problem, though the numbers are smaller than the hype would make it seem.

That being said, other countries don't seem to have the same issue, so it's still wild to have to try downplaying the violence.