To explain myself better now I am awake and have had coffee: What makes a cover that cannot fall down the hole that it is covering? The width[1] of the closed curve has to be larger than that of the hole. A circle is easy to understand because it is a closed curve of fixed width, but a Reuleaux triangle is also a closed curve of fixed width, meaning if that fixed width is greater than the widest part of the hole, then there is no orientation of the cover in 3D that will allow it to fall down the hole. It’s easy to see if you take an equilateral triangle, circumscribe it with the smallest circle and then (mentally) construct the Reuleaux triangle that the Reuleaux triangle sits inside the circle and so would use less material.

[1] This is defined as the minimum perpendicular distance between parallel lines bounding the shape.