That just has to do with the UVs and how they change after you go to subdiv...

See the two lines that are near the corner on the cubey one, then when you sub-d the lines spread out and move backward, this pushes the texture out so that it matches the original UVs, and thus you get the bends. This can also be seen that the side UV comes backward, thus putting a curve on the side line.

You might be able to take the UV layout of the sub-d model and redo the texture over that UV layout in PS, and fix it from there...then it would look odd in the polygon mode, but look fine in the subd mode...give that a try, no guarentees though.