That's the kind of Derridean approach to Criminal Justice that got us to where we are now. You're saying the same thing, though: a cities crime rate is entirely dependent on the policies of surrounding cities and not on itself. Think about what you're suggesting: even if NYC experienced a crime drop while also housing fewer inmates, it's only because their own policy was ineffectual and the surrounding cities picked up the slack (or something).
Indeed, many policies work locally but not globally. Harassing criminals and putting them on busses leaving town appears to work, but only locally.
Anyway, the story seems to say that since there was a period of time in which NYC crime decreased while NYC incarcerations also decreased, the theory that incarceration reduces crime is refuted. Hardly.
I live in a city where people are said to commute in from the outer parts in order to commit crimes, but the assertion is only ever backed up by anecdata.