A politician can neither be reelected nor avoid censure if the politician is involved in a scandal. In other words, if the politician is involved in a scandal, then the politician will not get reelected, AND the politician will not avoid censure.
On the other hand, let's assume it said a politician will only avoid censure if he is not reelected. In that case, it's an "or" rather than an "and". The politician will either get reelected or avoid censure. He can't get get reelected AND avoid censure.