Moving through subpixel sums will always change the texture selection. The fact that you use the closest selection affects the texture selection, but not the coordinate in which it is executed in the first place. This coordinate is a function of both tex-coords interpolated over the polygon and vertices that determine how the polygon is rasterized to display pixels.
Remember that in order to get the perfect texture selection, the interpolated tex coordinates, when they are estimated at the centers of the pixels, must lie exactly on the texel centers.
Moving the polygon to a part of the pixel on it changes where the texture is selected, since the centers of the pixels now lie at a slightly different point inside the polygon.
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