This is getting very interesting. Previously, Nanba-san punished Furutsuji for pressing her on her lies, and now in this chapter, Furutsuji is enthusiastically accepting Nanba-san's lies in order to keep her happy. This is Nanba basically getting what she wants, but it's framed as manipulation on Furutsuji's part. Who's in control here?
I think Furutsuji's read on Nanba-san's reasons for lying is only partially correct. Nanba-san does want to win the contest of who has it worse. She wants someone to express genuine sympathy for her situation. What she hasn't realized is that, although she's lying about being beaten, Nanba-san is experiencing very real abuse, just of a kind that's too shameful and embarrassing for her to want to admit.