Why does this plane's UVs distort when there is exactly one Subsurf subdivision level set? Why does the texture skew when you subdivide the plane once?
Each quad face is always made of 2 triangles in 3D softwares. I guess the result you see has to do with the way Blender will triangulate each of the 4 faces it creates when it subdivides.
Here I use a grid as image texture to make it more understandable. On the left, the original object, on the right, subdivided once. Here is how Blender triangulates:

If I select my original object, cut edges the same way to make only triangles, and turn the outline into a circle, I'll have the same result:

It would work better that way:

With a higher subdivision, the problem tends to be less noticeable.