Is “The direct cause of Yang Xiu's execution.” true?

The novel describes that Yang Xiu was executed by Cao Cao for revealing his intention to retreat in the 'chicken rib' incident, on charges of disturbing the army's morale (Romance of the Three Kingdoms, Chapter 72: 'Cao Cao angrily said, 'How dare you spread rumors to disturb my army's morale!' and ordered the executioners to take him out and behead him.'). In official history, the main reason for Yang Xiu's execution was his involvement in the succession struggle between Cao Pi and Cao Zhi. Cao Cao executed him to eliminate potential trouble (Records of the Three Kingdoms, Book of Wei, Biographies of Ren Cheng, Chen, and Xiao: 'The Grand Ancestor, having considered the changes from beginning to end, and because Yang Xiu was talented and resourceful, and also a nephew of the Yuan family, therefore executed Xiu on some charge.').