[heeton]

Time to get even more detailed :)

The article describes the opposite of what you did - grain usually aligns perpendicular to machine direction. After a quick search it looks like this is because of the Fourdrinier process commonly used, where a vibrating (side to side perpendicular to machine feed direction) mesh aligns the paper fibres as paper passes over it.

So this would explain the opposite of what you (and I) have observed with toilet paper.

Toilet paper is built on long rolls, then chopped down, so the perforations are also perpendicular to the feed direction of the roll itself. If this explained it, we would see it tearing more easily parallel to perforations.

Without researching more, my first guess is that the feed direction of the eventual roll is not the same as the machine direction for the paper that goes into it. And with multi-ply paper, do they criss-cross? I would presume so, for strength. You wouldn't want a finger break-through.

Now I'm wondering if there have been any rigorous studies into the orientation that people use with their toilet paper when wiping their arse...

[mkosmul]

The shake of the forming wire does help align the fibers in cross-direction, but the effectiveness of this is smaller than all the other effects combined, which align the fibers parallel to machine direction. So, overall, the process reduces the alignment to machine direction somewhat, but does not change it enough to make cross-direction dominant. So, everything makes sense: toilet paper is a long band, grain is aligned with machine direction (the long side of the band, perpendicular to perforation), and that's why it tends to tear "the wrong way". It was exactly the same with the paper towel whose picture is shown in the post.