CONCORD aren't just cops though. They're the United Nations of EVE, and seem to oversee multinational peacekeeping operations via the DED in places like Stain and so forth. It sounds like the empires still sacrifice elements of their armed forces to the DED to work alongside each other despite the state of war, or so the ISHAEKA reports suggest.
Even if they are just cops, CONCORD likely concern themselves with only the "interstellar" pirate factions listed in-game. There's hundreds and thousands of smaller threats that the empire's national law enforcements would deal with, even just 'generic pirates'.
In addition, the DED takes care of all kinds of security issues regarding meetings and conferences between the empires, they lend ships for operations by the other branches of the CONCORD, and they often support local law enforcement in dealing with large-scale criminal activity or similar matters. DED ships are equipped with the latest surveillance technology and are considered a great support for customs patrols. The DED’s jurisdiction is limited to space but in recent years they have been authorized to operate in stations and on planets.
From that, CONCORD's law enforcement and military authority is not all-encompassing, so the suggested dichotomy of "bad CONCORD" versus "good local cop" is not always necessary, since CONCORD won't be messing with local policing.
"Incorruptible" could be assumed to mean "very low corruption rate compared to the empires". Given their use of Jovian technology, anyone found to be corrupt could be weeded out extremely quickly. Again, if they're not answerable to anyone but themselves, then my imagination fails me as to why they would be corrupt in the first place. "Corruption" seems a very loosely defined term anyway. If we mean the major pirate factions penetrating CONCORD, that would be quite the feat, given the advanced technology and their monolithic, highly centralized nature (excl. Sansha). The empires themselves would be far more susceptible to corruption, especially decentralized factions like the Fed and Amarr.