I have medium crown authority, why are my vassals still fighting each other?

As I understood, crown authority from medium up should prevent vassals from figthing each other. I am playing as King of Scotland and Ireland and have medium crown authority, still my vassals are still figthing in almost every corner of my kingdom. Have I misunderstood the meaning of crown authority's description?

Some of your vassals will fight each other because they're fighting a war of independence: one of your counts has revolted against one of your dukes. Check the character screens of the people in the war to see what wars they're currently in.

This is exactly the same sort of war you get when one of your dukes/counts hates you sufficiently. (Being on the far side of the world makes rebellions more likely; Jerusalem isn't such a prize if you're in England.) In the "Intrigue" screen, the "Threats" tab tracks these problems, but only against you, rather than against your lower vassals.

Also note, that ongoing disputes won't end automatically when you raise the crown authority.

I believe there are several reasons for this:

• they are not your de-jure vassals, crown authority applies to de-jure vassals
• the war was started through plot, those are not limited by crown authority