As you can see below, when I select the mesh that uses my material the transparency works, but when I deselect the mesh or render the scene there is a halo of color around the black lines on the texture.
The color matches the background of the scene regardless of the color, so it doesn't seem to have anything to do with the texture itself. I've got similar textures working without this problem in other blend files.
Edit: I've also noticed that even the grid lines are visible. It's like the transparency mask is ignoring the mesh directly behind it right around the black lines in the texture.