There are a couple of humorous anecdotes in this article on Kikar about Chief Rabbi Yitzchak Yosef refusing to meet with the Gaavad of the Eida Hachareidis, Rav Tuvia Weiss.

According to the article, and in a news blurb I saw elsewhere, Rav Weiss called Rav Yosef to  secret meeting, yet Rav Yosef refused to go to him for the meeting. Rav Yitzchak Yosef said, in his weekly Motzash shiur, that Rav Weiss called him in to talk about why Rav Yosef recently said that the Eida is the worst of the hechshers on meat and Sefardim should not eat it at all. Rav Yosef said, he called him in and said he is willing to accept me to talk about it - thank you, he wants to tell me the hechsher is ok. Rav Yosef repeated that the Eida is the worst [on meat]. Rav Yosef previously said people should rely ont he Rabbanut hechsher and strengthen the Rabbanut and not add on with other hechsherim (specifically the Eida, but if he says Rabbanut is good and we need to rely on it and strengthen it, he must mean against all other hechshers as well, not just Eida. Even his own family's Beit Yosef hechsher).

Another thing he said is that Rav sent a messenger beckoning him to come for a meeting at midnight with no cameras. He said he refused - what do I need to go for so after they will put up signs about me?

Another interesting anecdote related is not about the Eida, but about its close cousin, Satmar. Rav Yosef said that one of the admorim of Satmar came to him but was worried about the meeting being made public and it would end with him being attacked as a Zionist. Rav Yosef says he responded that you have nothing to worry about because the position of Rishon Letzion has existed for 350 years [and has nothing to do with Israel or Zionism] - if you would meet with the Ashkenazic Chief Rabbi, then you should be concerned because that position is a State-mandated position.

That last one is funny. As if he was not appointed by the politicians and rabbinic leaders of the State of Israel to this position. As if his chief rabbinate position is not an Israeli office with budgets and salaries paid by the Zionist state, with authority granted by the Zionist state. As if the Sefardim in general, including the rabbis and him and his family, are less Zionistic than the Ashkenazim.