This is very true but it's also a little misleading to the layman. If we look at the murder balloons for Chicago they are dominated by the following areas, Garfield Park East/West, Fuller Park, Englewood, Greater Grand Crossing, and Washington Park. Chicago has a population of 2.7 million however these neighborhoods have a population of only 116,000. If we use the per captia then we are looking at a 1.16 multiplier. If we take a conservative estimate of only 50% then we have (taking 2015 as reference) (.5*507)/1.16= 218.53 In this we now have a "Murder rate" of 218 (which isn't really true this is a homicide rate murder rates are often difficult to pinpoint due to the data collection process.)
Now, remember, this is at "best case." In all reality, we would probably be north of 60% of all murders located to those areas. Even if we double the population to include the immediate surrounding areas and apply we have (.5*507)/2.32 we would still be at 109.27 murder rate.
That's the reason why it's such an issue.