I think there's some (understandable) confusion regarding Brightest Day. Though BD the bi-weekly series sprung out of BN, it has very little to do with Johns' overall GL arc. Now, there is a GL arc titled "Brightest Day," much the same way there's a GL arc titled "Blackest Night." However, unlike BN, the GL arc titled "Brightest Day" has very little (if any) to do with the bi-weekly series of the same name. They just happened to be coming out at the same time.
The GL omnis, which obviously don't include the BD series which got its own omni, read as a cohesive whole and don't require the reading of the BD series. Hope this made some kind of sense.