Yao is merely worried that a third party will see the truth of the matter ; that those islands belong to Japan.

simply wants to keep this between the two of them, bringing America into it is unnecessary and will only bring about more problems.

America is involved in it anyways, considering his involvement still in Japan's government.

doesn't believe that at all. This unfortunate incident is between Japan and China, there is no third party. The offer will remain declined.

knows that this is only between them, but also believes a third party mediate would be a good idea.

just doesn't like the idea, and will continue to respectfully decline.

(respectfully) continue to think that Yao is stubborn then.