The ability reads SHE is immune, however, what about Terror affects that'd add another doom token, for example? In that case, the Terror effect wouldn't directly target her, would her immunity still cancel the effect. Or if an effect states All investigators lose 1 sanity/stamina/trophy/etc. Would the other investigators still be affected.
Kate Winthrop's ability should be played as if the terror die does not trigger the terror effects. So, no doom should be added, nor other investigator should suffer any effects. I could not find rules about that anywhere, but that's how things work in the mobile version of the game.
I would be wary of letting the mobile app too strongly dictate inferences on how the base game works. There are clear differences between the app and board game such as the locking of dice using spells which does not carry over after a character locks a die in the app but does so in the board game.– JoeyJun 23, 2015 at 20:23
That said, I agree your explanation is simple and clear. The only thing in question is whether another investigator triggering terror effects can cause her to suffer from them. If someone effects "all investigators lose 1 sanity", do all but Kate lose 1 sanity in this case?– JoeyJun 23, 2015 at 20:30