I'll be the first to admit the city cleaned up a lot between my first vist there in the late 1970s and more recently a year or two ago ... that said, for whatever reason, a lot of non American first time visitors seem to still carry that '70s image of NYC as a crime hub.
Might be all those 'classic' NYC films exporting a vibe.
I still haven't seen an NYC rat chase a cat while carrying a pizza though, admittedly I'm an infrequent and short term visitor.