Fox News and their siblings (NY Post, WSJ mainly editorial, etc) have been running with the NYC is over narrative for quite a while. Especially the 'more dangerous than ever' trope. And they always talk about moving to TX and FL where the large cities have a homicide rate 2 to 4x what NYC's is.
I honestly think the main culprit is local news. They're essentially non-journalists, so they basically cover violent crimes as sensationally as possible.
I have relatives in red states who ask me how I can live somewhere as dangerous as NYC. Meanwhile, they're living in a metro area with triple the homicide rate of NYC.