If that map is accurate (and I am not saying it is or isn't) there are plenty of high population areas that are red and not higher in crime, and a good portion of high crime areas that are not really large population centers (like New Mexico, for instance).
And plenty of blue high density regions that are blue and low in crime as well, but the generalization is more often true than not. I was mocking the crime "declaration" more so than the crime/rate per capita which would've been the correct metric.