I just realized a plot hole. It's fact that Jon knows the white Walkers are coming, he's seen them and they need people for the War. With Brienne being in the same camp with jon and the Wildlings/Rangers it is likely she was told about the threat and how they need help. She goes all the way down to RiverRun where there are 3 ARMIES - Tully, Frey and Lannisters, hmm, what would be a good way to get the Lannisters to back down from the Siege, what would be a good way to get the Tullies to leave their Castle... If she had just mentioned that, I'm sure the Blackfish would of went with them and took his army, which Jamie even said they could leave, and I wouldn't be surprised if she managed to persuade Jamie as well. But no... This is actually annoying me now, the Writing has degraded lately.