True, they look at the news and not the actual figures that show the USA is statistically far more dangerous.
But Britons from outside London ask this too. What everyone who asks this forgets, whether American or not, is that you have to put it in perspective. In a city of 8 million or more people, there will be crime, but murders are so infrequent that they make news. If they happened all the time, they wouldn't be news. To make news, an American murder story needs to be unusual, more shocking than usual, or involve a lot of deaths like that recent mass shooting in Las Vegas.
To put THAT one in perspective, the last time the UK had one of those was over 20 years ago in Dunblane. (Fun fact: Andy Murray was in the school at the time, just not in the class that was attacked. How nice it is that he's given his home town something better to be famous for.)
Same for the question of whether it is safe to fly - air crashes are so infrequent and so many people get injured or killed when there IS one that it always makes a big news story. Far more people die in car crashes, but they happen all the time so they're not interesting news. So as is often said in the Air Travel section, you may be scared of flying (and thousands of feet up in the air with no visible means of support is not a natural place for a human being to be, so naturally it scares some people), but the truth is you are far more likely to die in the car on the way to the airport! Not that this really helps anyone with a fear of flying but it's a fact.