Kirk, Spock, and Uhura would have no reason to go to Kronos other than to follow Harrison there. And that's as far as I can get with it.
If Harrison is a betrayed Klingon spy, there better be a scene in the movie where McCoy says, "Jim, this man is a Klingon!"
Now if you'll excuse me, it's lunch time. Eating trigger. Every time I see Qo'nos, I think of Quiznos.