Even many samurai, regardless of their rank, would often quote phrases from Chinese classics like The Analects, Zuo Zhuan, or Records of the Grand Historian when giving advice or writing documents—so fluently it was almost infuriating. Composing Han poetry was even more fashionable, seen as a mark of deep learning.
As for hiragana and katakana, they were not widely popular in this era. At most, they'd be mixed into linked verse or everyday letters. If you used too many "kana" in an official document, someone might well laugh and ask, "Are you a woman?" After all, in this age, "kana" mostly circulated among Japanese noblewomen, mostly court female officials using them for convenient shorthand—a sort of cursive Chinese script.
So, there was a ninety-nine percent chance that Okumura Iefuku had read Chinese histories, knew about the deeds of rebellious sages like Zhang Jiao, and was well aware that medicine and witchcraft were definitely tools to incite rebellion.