Seems like a z-buffer issue.
Everything seems fine in the material preview, but in the render the sky (or transparency, if no sky) "bleeds" a pixel or two between the intersecting part (intersecting in the 2d render, not 3d) transparent textured geometry and any geometry behind it. Hope this makes some sense:
Changing transparency mode of the Texture from Straight to Premultiplied doesn't fix it.
blend can be found here: https://drive.google.com/open?id=0B8pm58kHwzU3M3hUZmdFdUhTdDg
The texture file separately can be found here: http://i.imgur.com/bRBRdX8.png Tried a different texture file from cgtextures with no difference.