According to the government's logic, the Chief Rabbis are appointed byt he people because they are appointed by people who were voted in by the people - ie, the politicians were voted in by the people and they choose the Chief Rabbis, so the people basically chose the Chief Rabbis. On the other hand, the judges choose themselves and were not selected by people voted in by the people (which is not accurate, but not the point) so the judges are not chosen by the people. 

Alshich was appointed by Netanyahu and his government in 2015, so by extension that means he was chosen by the people. So if Alshich is against Netanyahu (which isnt clear) does that mean the people, and especially the Likudniks, are against Netanyahu, and maybe even Netanyahu is against Netanyahu? I am scratching my head over this.

Regardless, they are turning Alshich's words into something very dramatic. What he actually said is far less so. Alshich did not say that Netanyahu was framed or that he should have done this or that or that they tried to push him out. All Alshich said was that when they served the indictment nobody expected him not to resign. That is not a big deal. Everyone, and not just the legal word of Israel, but many citizens as well, expected him to resign. Let's not forget, Netanyahu himself said in the time of Olmert that a PM under indictment must resign. Most reasonable people expected Bibi to resign on indictment. That does not mean he was or was not framed. 

Alshich's words are not nearly as dramatic as they are being made out to be.