In this sense "adversarial" has the same meaning that it does with respect to the relationship between the defense and the prosecution in a courtroom setting -- the best outcome is going to be achieved from the equilibrium of distinct organizations with incentives balanced against each other.

It's precisely because of the importance of policing that we don't want the people responsible for oversight and discipline of the police to have a "solid working relationship with faith and trust running both ways" -- there needs to be an arm's length relationship, with the watchdogs incentivized to monitor for wrongdoing, and the police somewhat afraid of being called out by them, certainly not buddy-buddy with them.