ugh. spurious reasoning
When areas or situations are unsafe people must make compensating behaviors to protect themselves because nothing else will protect them. They don't go out at night, they don't go out alone, they avoid looking like they have valuables, they especially don't go out at night alone with valuables while being a woman. They take longer routes to avoid worse places, they don't make eye contact. They carry weapons. They change to the other side of the street.
The effect of these compensating behaviors is that the recorded rates of crime go down and can continue to drop even as the level of safety and imposition on people's lives goes up. In that case they're not more safe, they're less, but they're not relying on the people whos crime stats we look to for as much protection as they did... which brings me to:
Another reason drawing this connection can be fallacious is because in areas of persistently high crime people don't report it because law enforcement will not do anything about it (or won't even take a report). Exceptional events are worth reporting but when a kind of crime is common it's not an exception, reporting is just a waste of time for everyone involved. Again, reported crime can go down while crime is going up.
Yet another reason why these figures can be misleading is because the nature of the crimes can change. In one location most shootings may at one point have been drug dealers shooting each other in turf wars, but later they begin shooting uninvolved residents as part of robberies. While its terrible that anyone is getting shot, criminals shooting each other is rightfully less of a concern because it has the obvious personal mitigation of not being involved in the illicit drug trade (for this example...). So yet another reason why you can hear from people that they are less safe even when the stats say crime is decreasing-- essentially simpsons paradox: the way you aggregate or disaggreate data can swap the direction of a trend. No person experiences the population's crime rate, each person experiences their own crime rate.
And sure there are also plenty of effects in the other direction too-- the 24 hour news cycle, open records laws, social media feeds, ubiqitous cameras-- all making some people feel like they're in the middle of a warzone even when they're perfectly safe. But the existence of biases in one direction doesn't make the other not exist. And for some people and places the net bias may be one way while for other people and places its another.