Don't think it's luck, there are areas inside the communes that are better than other, for example, i live in Puente Alto in a place you could say it's middle-upper class, unless i'm living surrounded by narcos all the nice houses and cars are from people with income higher than average.
But in puente alto you have areas like El Volcan and El Volcan 2, Bajos de Mena, Carol Urzúa and a lot more, the area limiting La Pintana is some shady shit, needless to say, La Pintana is also super shady.
I remember visiting some friends in Peñalolen some years ago, near Grecia avenue and Tobalaba and we went to buy some booze, if we weren't with my friend at the time, five dudes in a corner would have mugged us.
To answer you, there are some fucked up places to walk alone in Pudahuel, Cerro Navia, Quilicura, Conchalí, Maipú, La Pintana, San Bernardo, Santiago Centro (Had to escape a a robbery attempt there), Puente Alto, San Joaquin, La Granja, El Bosque, Quinta Normal and La Florida. But all of them are quite specific.
While I agree with you on some problems being worse than crime (I'd add Public Healthcare), there are things like crime stats that shouldn be sweeped under the rug.
https://en.wikipedia.org/wiki/Robbery#Robberies.2C_by_country
(Sorry for citing Wiki)
We're not Belgium but we're pretty up there