Removing Investigate Legitimacy would cause all kinds of problems. We kind of need it for there to be any chance of the War of Five Kings starting organically. Plus, it also doubles as a plot to fabicrate evidence that the official heir is actually illegitimate, which is a pretty classic feudal power play.
That said, what exactly do you mean by "people with 100 opinion of you" in this case? People with 100 opinion of the target, or with 100 opinion of the target's alleged father? The former is what I'd expect, and would suggest that the AI needs a rework, but the latter is what's implied by the reference to Ned and Jon Arryn (no way in hell they had 100 opinion of Joffrey) and should be fine, since in that case they're really just concerned about your dynasty.
I do agree that Purchase Loyalty needs to be removed, or at least majorly reworked. Several things about it simply don't make sense.
One hundred opinion of the alleged father.