I think "I don't know" works well because at the core you're refusing to play the game. Politics can't hurt you if you don't let it.

Mostly, I've found that if you stick to the facts, clean and simple, and avoid the games, those intent on playing get disarmed quickly. If they can't get to you, they can't force you into a corner and so, often they can't win. Sure, on rare occasions it may cost you a job or two, but only in organizations that are political anyways. If you don't like being paranoid, then a nicer environment is actually a good thing.

In the end, I always try to do the Right Thing regardless of the consequences, and then let the chips fall where they may. Staying out of the game is the only way to consistently win the game.