That is a fairly good example since it also applies to tangent space normal maps.
Say you have a normal map for a sphere. the X channel will be the “side to side” gradient, Y channel will be “top to bottom gradient” and the Z channel will be “Front to back” gradient. But you lay down that normal map on the ground, and suddenly the Z channel is actually pointing up into the air, off the texture sheet while X and Y are planar to the mesh surface normals.
so in the case of a mesh laying on the ground like that, a transform tangent to world would not actually do anything (assuming the X,Y directions were right), since the mesh already happened to by laying with its local tangent vectors aligned to the world space axes.