Is “He would rather be Cao Cao's slave than Liu Bei's guest.” true?

attested in history

The Records of the Three Kingdoms, Wei Book, Biography of Zhang Lu records that when faced with Liu Bei and Cao Cao, he said, 'I would rather be Cao Cao's slave than Liu Bei's guest,' and then surrendered to Cao Cao and was enfeoffed.

Zhang Lu

In official history, he was the third Celestial Master of the Way of the Five Pecks of Rice and the leader of a separatist regime in Hanzhong.

Other claims about Zhang Lu