The reason this storyaboutanaffairbetween Yoshitsune and Kenreimonin appeared is due to itbeing mentioned in 'Genpei Seisuiki' (The Rise and Decline of the Minamoto and Taira Clans).
Wikipedia日英京都関連文書対訳コーパス
『偐紫』の『紫』は、紫式部にも高級染料のムラサキにも通じる。
The word "Murasaki" in "Nise Murasaki" refers to both Murasaki Shikibu and gromwell, the high-grade dye.