Sengoku really is a b*tch. For one, using the farce of Nanao and Fuji being in a relationship as an excuse to deny being Fuji's girlfriend really pisses me off. What an effing ice queen.
Secondly, she could easily have stopped Nanao's shenanigans, but I guess she doesn't care enough about Fuji considering the fact that he just got out of the hospital (having nearly died because of her cooking), but she is fine with playing along with Nanao at Fuji's expense.