To clarify, here is the alpha channel for the DXN_jungfx texture:
If you look closely, you can see that the background for three of the four parts is not completely black. And for some reason, some ATI cards won't render anything behind these parts of the grass. In other cases, the grass was not mapped properly, so bits of one texture show up at the top of another as awkward lines well above the ground.
However, there's only so much I can do with the textures due to the incredibly poor resolution. When it's rendered, the texture is smoothed over so it won't look so pixelated, but unfortunately that leaves behind an invisible halo around the grass when it's seen up close, or when a lot of grass is obscuring something far away.