I'm not asking this to be a smart-aleck Dave, but don't we already have that in Batman?
Dave's right, and not really(the Batman thing). Batman doesn't trust ANYBODY, that's true, but GA should be that moral compass that sits on the outside looking in. Where Batman can still see the League as a tool to provide a means to his ends, Ollie, TRADITIONAL Ollie, was born into comics as the mouthpiece for the people. Even those original GA/GL stories gave us a GOD (GL) tempered by the social constraint and insight of the common man (GA). Batman considers the rest of the JL peers. Ollie sees himself as the odd man out who's there to make sure 'the Man' doesn't take advantage of the people. He's just a guy, but through training, wit, and perseverance he can keep up with the Big League enough to keep an eye on them and will be the first to point out the emperor's clothes.
Of course Dave'll put it better, and Ollie in the comics will probably end up more like the CW character anyway so this will all be moot