In the (admittedly unlikely) case that a poll is off by so much that even the margin of error is insufficient to make it correct, while still having been correctly executed, the statistic does for all intents and purposes lie.

More often, statistics "lie" due to not having been executed correctly, most often I suppose by failing to have truly independent data points, or perhaps for other reasons.

But it's true that statistics being misreported or misrepresented are still more frequent than either of the above.