The way I see it, Cochran wasn't going to win anyway. He can't win challenges, and once the other tribe was gone, he would've been picked off right away by his own tribe, because in that scenario they wouldn't want him in the Top 3 for fear of receiving "underdog" votes.
So now, he might actually proceed further and get to the Top 3 because everyone knows he won't get the votes to win after pissing off his former tribe. So in that sense, he's going to last longer in the game.
But this really all goes back to the boneheaded decision that Ozzy made last time out. Sure, he won at RI and got back in the game. But by keeping Cochran around, they have pretty much fucked themselves. If they had ditched Cochran last week, Christine would have won at RI and re-entered the game. She would have hooked up with Ozzy's tribe, and based on the odds, they most likely would have come out of last night's TC on top.
They have no one to blame but themselves.