@Ciel
Southern Kai was behind all the crap Kouka was going through, in Awa, in Sensui, in Suiko. Kai denying means that it wasn't an official disclosure, nor an offer from them on the table for "make believe diplomacy", that "yes, we've heard, and we'll try to curb the Kai traitors so that both our countries can prosper.".
Instead, they denied, believing they still had the upper hand and that they are still making underhanded money, and gaining underhanded control of Kouka's territories.
But because Yona mentions that, oh, FYI, we stopped all the shit you were doing to Kouka + we have some prisoners, meant Kai lost out on their black market profits + have the risk of tattle tales.
See also Kendama's comment on pg 2 in the other translation discussion.