2DTexture "lines" despite clamp & no mip-mapping

I've got a procedurally generated surface, consisting of many tiles. I'm also procedurally assigning UV coordinates to each tile which determines their type (grass, sand, dirt)

But even though I'm certain the UV positions are precise and correct I still get a little bit of "bleed" from adjacent squares in the texture image:

http://i.imgur.com/wo2qHkG.png

As you can see I've got the wrap mode set to clamp and no interpolation set.

When I change the adjacent tiles in the texture image to solid purple or something the lines become distinctly purple, so I'm certain it's color bleed, I just don't know how to fix it and why it's happening considering the filter mode is "point".

Edit: To be clear, all tiles you see are part of one mesh but each tile is it's own 'square' within the mesh, i.e. 4 verts, 2 tris. Also the texture is a 512x512 png and each 'block' in the texture is 32x32 pixels.

(And yes I'm using a minecraft texture to test with, but no it's not a minecraft clone ;))