You're right and wrong. The first paragraph is absolutely accurate -- I live near some of these areas (SW Connecticut) and the contrast is stark.
The second is not. There are absolutely people who take pleasure in the bullying behavior cops are often associated with. They're the ones who want the cushy jobs in Greenwich but don't get them (probably for the aforementioned reasons in many cases) and wind up being doubly punitive and cruel to people in Bridgeport.
Violent crime / property crime per 100k people:
Bridgeport ~393 ~1,700
Greenwich ~9.4 ~867
More cops, more crime! In other news, wet sidewalks cause rain.