@jokerxhisoka He could say he knows her because they met somewhere and became friends or dated. He may risk something, but I think his position is definitely safer than Yoshida's since he is the one currently living with Sayu and there are witnesses.
It's true that Sayu is already involving Yoshida since the beginning of the story but now she is facing a concrete threat that in the worst case could lead to him in jail. Of course she wants to avoid that no matter the cost.
I agree that caving to blackmail isn't a wise choice, since it will only lead to being blackmailed more, but given that the entire situation was so sudden, I can't fault her for not acting in the best possible way.