Fujiwara no Saneyori was a real person. As the novel shows, Saneyori served as Sadaijin (Minister of the Left) for Emperor Murakami, and he later served as Kampaku (a combination of Regent and Chief Advisor) to Emperor Murakami’s son, Emperor Reizei. Saneyori was extremely powerful in the political sphere even before he became Sadaijin. He served as Udaijin (Minister of the Right) earlier in Emperor Murakami’s reign.
There is no doubt that Saneyori was quite powerful in the politics at the time, but whether he and Emperor Murakami had any sort of conflict is unknown, and therefore the conflict in the novel is fictionalized. There is evidence that Emperor Murakami sought to lower taxes on the people, as in The Accidental Samurai, and that this attempt was resisted. Whether that resistance came directly from the Kugyo, as in the novel, or from local officials, is unclear.