Is “In the novel, Pei Ji is depicted as a eunuch, while in official history he was a prime minister in the early Tang Dynasty.” true?

The 'Old Book of Tang, Biography of Pei Ji' records him as a leading official and founding minister of the early Tang: 'Pei Ji, styled Xuanzhen, was a native of Sangquan in Puzhou.' The 'Basic Annals of Gaozu' records that in the first year of Wude 'Pei Ji, Chief Administrator of the Chancellor's Office, became Right Vice Director of the Department of State Affairs,' and in the ninth year 'Pei Ji, Left Vice Director and Duke of Wei, became Minister of Works.' Yet 'Romance of Sui and Tang' (chapter 017), describing the lantern festival in Chang'an, writes: 'Two grand eunuchs sat on silver-flowered chairs -- on the left, Pei Ji of the Directorate of Ceremonial; on the right, Zong Qing of the Inner Inspectorate.' It not only turns a Tang chief minister into a eunuch but also borrows the Ming-dynasty office name.