It cancels out the tapestry because the "invisible skirt" has transparency, and is in front of the tapestry,
and the tapestry itself has transparency.
The tapestries have transparency, so that they can be "see-through" at the edges of the mesh,
so that they look like hanging cloth in-game, rather than like a stiff rectangle.
(Some of them also use this to have holes and rips in the fabric, so that they look old and worn-out.)
Transparency in Morrowind is achieved through the use of what is known as "alpha-channels".
Due to the way Morrowind's graphics system works, two alpha-channels cannot overlap.
As a result, if one object with alpha-channel rendering passes over another, the second one loses it's alpha,
and disappears, at least in the part that is covered by the first object.
Blame the system for not being capable of multiple transparency layering.
I hope this was at least informative, if not helpful.