Ovinomancer
No flips for you!
Sure, it could get hard for the player to continue to RP, but there's always options, and the onus is entirely on the player to figure out how (although hopefully the other participants would enjoy the character enough to make helpful suggestions in the tricky spots). "Because I'm a genius, I easily resist the evil sorcerer's Truth Magic, and I tell her that I don't know the answer." And that's ok because it's the exact same outcome as not knowing the answer and failing the saving throw.
And what happens when the character does know the answer to the next question the evil sorcerer asks? You keep digging holes, man. I dig where you're coming from, but the specific choices you've made are inconsistent and incapable of being followed outside of a range because they're kludges on the system, not solutions. Better to find a better reason than 'I defer to my tiger, that's why I act stupid, I'm really a genius'. That falls apart when there's no tiger.