Rei, I think you might be ignoring the gyroscopic force caused by the earth's spin that would make it so resistant to tilting that only a mass of ridiculously immense proportion could alter it by gravity alone. Even then, gravity's pull would be distributed across the whole planet more or less equally instead of only on one particular half of it.
I think that if a mass of the required size ever passed through the vicinity of our planet with enough proximity to tilt its axis in any meaningful amount it would also have obviously observable effects on the rest of the planets in our system. Hell, I don't know what the calculations might reveal, but I wouldn't be surprised if it required an object with greater mass than the cumulative mass of our entire solar system -- sun included.
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