This is exactly the way I see it. Assuming a constant firefight is totally unrealistic. People live here, and even the most crazed lunatic wouldn't choose to live around a constant battle, (if for no other reason than they would not 'live' there for long until they were a casualty.)
Look at the favellas of Rio, plenty of ordinary people lives and work here caught in the crossfire of narcogangers and crazied paramiltary police (This is the land of infamous police deathsquads ) Even more cynical, the rehabilitation of the favellas for the world cup showed some serious flaws, the police force was involved in many crimes in thoses areas: becoming the main gang around, they started to control the turf and making illegal street money.
As in real life, the combat zone is full of normal people struggling for a living in a "grey" area full of contradictions, with criminals and borderline cops chasing around and a regular collateral damage toll on the street people. Here, nothing is really sure because things change everyday: people dies easily, businesses disappears in a blink, the gang next door is on the verge of extinction, your car was stolen right now, ... When you're in the CZ, it's kinda Twilight Zone, gato, people are strange and nightpeople dangerous.
As fixer says, the city have a pulse, a rhythm, a mood you can feel in your bones if you belong to the city (In fact, it was Michael Man, in most of his films you can feel this city pulse. The opening night sequence of Abel ferrara "King of New York" is also a great one).