I think, without being starship captains, it's hard to imagine how incredibly pissed off and anxious Captain Kirk was because of the priority distress call. The last time there was a similar situation was when the Romulans attacked the outposts along the neutral zone. I think Kirk was fully expecting Klingons to be attacking the station, possibly having destroyed it by the time they got there, and finding nothing wrong, in his opinion, diverted all of that tension and adrenaline into the kind of behavior he had. So, it doesn't seem wrong to me.