If you knew why Lin got promoted after the collapse of Liu you would reach a totally different conclusion. Zhou and Liu were ally before the Great Cultural Revolution, and Lin helped bread the balance because Mao wanted to grab the right again. After Lin agreed with Mao in forming their own ally, he sent army into Beijing and controlled the forbiden palace. Lin and Liu got beaten, but Mao did not have the capacity to crumple down both Liu and Zhou, and Zhou had huge support from army force and executive side, Liu was then the only choice as a culprit.
Many researchers tended to overlook Zhou's force. If he was so weak, he would have been removed from his pole long time before the Great Cultural Revolution.