This is why LiuLaoDa is a top level leader to those leaders. He got what he wanted but leaving the bad name to others, his wife and Han and Peng and Ying.
Same happened recently in the case of Chairman Mao and his wife, JiangQing. It left a final option for Liu and Mao when they ought to make a 180 degree turn around.
I think the fact that Han and Peng and Ying were all killed under name of rebellion is worth a more detailed study whether it is duo to Liu's personal idea or systematical conflict among them.