Let me ask a question.
Are you sure you're seeing the starfield0000.dds texture through the planet texture (probably the shadow side of the planet, hmm?), or are you seeing the retail stars rendered on top of the planet? Could you post a screenshot of the issue?
Because retail stars are rendered on top of skyboxes, and starry planet sounds exactly what the FRED2 defaults to. You can edit the mission file(s) in any text editor to change the number of retail stars to zero (I believe the minimum that FRED2 lets you set it to is 500...). This an issue that you will have if you don't fix it, regardless of whether the textures actually work or not, so I suppose it's worth bringing up even if that's not what you're referring to.
If you really see the actual starfield texture through the planet, I would guess that you have managed to make black colour transparent in the planet texture, whereas in actuality you would want the shadowed side of the planet to be black with 100% opacity, and only make the edges of the square (and atmosphere partially) transparent, like in Water's example.