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I don't think it has to do with balanced quadtrees (someone correct me if I'm wrong).

When a value in the heightmap represents the height of a quad, then it is convenient to make the width and height of the heightmap a power of two. However, the value in a heightmap typically represents the height of a vertex. In that case, it is convenient to make the width and height of the heightmap a power of two plus 1, since the number of vertexes is one more than the number of quads. As you can see:
    *---*---*    |   |   |    *---*---*    |   |   |    *---*---*

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