A household flatbed scanner head doesn't have a CCD the full width of the scan. (I suspect, most of them don't). Instead, it has a fairly wide angle lens and a narrow mirror (or two) which concentrates the image on a much smaller linear sensor.

I should have one in pieces to show somewhere, but meanwhile a schematics could be found in this article:

Consequently, it has all the problems of wide-angle (or any) lenses, including distortion. And this distortion is non-linear, in the sense that the edges may be stretched relatively more than the centre. Like cameras, some scanners might compensate for it, some don't; in any case, the horizontal (cross-wise) resolution is only approximate.

At the same time, lengthwise resolution can be made highly accurate and linear. It's just a question of good mechanics, and not expensive at that. Lengthwise distortions are typically the missed or repeated lines due to some random glitches, and they are rare.

This can be easily observed by scanning something round, such as a CD. It never turns out the same pixel dimensions across and along, and scaling one dimension to match the other will not make it perfectly round (try with a circular mask).

Unfortunately, I don't know of a distortion correction filter that works only in one dimension. It can be improvised without great difficulty though. I never needed accuracy greater than what linear scaling gives, but lining it up like you do may require it.

P.S. If the paper is white, why not just blow it beyond highlights?