Yeah, Hal got a ring separate from Sinestro's there, but had his encounter with Black Hand immediately after that, leading to where he is now. There's not time any way you swing it. There was no time between Brightest Day and War of the Green Lanterns, either. The storyline with Hal hunting the entities led directly in to WotGL. Unless Justice League's second arc took place directly after Blackest Night, which it really couldn't have neatly, we're just going to have to accept screwed continuity for Green Lantern. It wouldn't be the first time that the New 52 has asked us to accept that.