I suppose as a king, you will have all your vassals fighting for their own titles between them. In this example, the king attacked a bad vassal and give a reward to a good one which appeared to have the claims, so he doesn't mind about the tiers that are below unless one of them threaten him. If the countess (now duchess) would have intriged to become Scotland's queen, no doubt he would have crushed her.
Essentially, I think a king should worry when all is too calm in his kingdom, because that means either that no-one has any ambition or that they are planning to give him trouble. This is counterweight however by the fact that you know what are your relationship to those people. So basically, you have to worry about people from your rank or just below you, maybe also if a character is really successful, but you won't have to interfer if you are the HRE in a plot created by counts of nowhere about the poor duchy of whatever.
I think it should be the other way, in times of prosperity there is less need to be cutthroat and scheme for more power and land, in times of hardship though you will be in extreme danger because income is more scarce.