Even many samurai, regardless of their status, often cite phrases from Chinese classics like The Analects, The Zuo Tradition, and Records of the Grand Historian when giving advice or writing documents, skillfully so, and composing Chinese poetry is even more fashionable, symbolizing profound knowledge.
As for hiragana and katakana, they were not popular in this era, at most mixed into linked songs or everyday letters. If you use too much "kana" in formal documents, others might jokingly ask you, "Are you a woman?"—in this era, "kana" was mainly popular among the aristocratic women of Japan, mostly used by palace female officials as a convenient shorthand, a cursive form of kanji.
Therefore, there is a ninety-nine percent chance that Okumura Iefuku has read Chinese historical books and knows about Zhang Jiao and other rebel sages' deeds, clearly understanding that medicine and witchcraft are definitely tools to incite rebellion.
