Why Can't A Rabbi Respond To The Police Summons?

There is a lot that can be discussed regarding the arrest of Rav Dov Lior yesterday. There are many aspects to the incident worth discussing, such as; the State's clamping down on halachic discussion, Rav Lior only wrote approbation to book and is not the actual author, why is this such an issue, freedom of speech, incitement, who is above the law, and more. I only want to talk about one point from this whole situation. That is, why could Rav Lior not go in for questioning.

I am not saying Rav Lior should have been arrested, not even saying he should have been called in for questioning (he should not have been), and it looks like the State was looking to pick a fight (I dont know if they were or were not, but it looks like they were).

After all is said and done, whether right or wrong, Rav Lior was called in for questioning by the police and he refused  to go. He did say, to his credit, that he would answer questions if they came to him, so he was not turning it into an anti-State issue, but he did refuse to respond to the police summons.

So I was thinking about this and I could not come up with a satisfying understanding of how this works. Why is it that a rabbi, and Rav Lior is not just any rabbi so I am not asking about him specifically but because of him, thinks that he doesn't have to go to the police to respond to a summons. I don't think rabbis think they are above the law, rather there is some organic respect that must be afforded to the bearer of the title that would excuse them from such "common" things.

So what is it about the title "rabbi" that makes people think they are excused? If a person was old, frail and infirm, I could understand asking the police to come to that person's house to ask the questions rather than making him go to the police. But just because the person bears the title "rabbi", why can he not show up to the police station? 

I bear the title rabbi before my name, though nobody uses it except for my mother (hi, Mom), so if the police should call me in for questioning about something, could I create a ruckus and refuse to go? What kind "rabbi" can do this? any rabbi? a teacher? a rosh yeshiva? a city rabbi? a shul rabbi? Who has to respond and go to the police, and for whom is it considered disrespectful?