I have a sphere which uses a script to reverse the winding and colour it white on the inside. I am then using a projector to project a texture onto it. The texture is an orange circle on a black background, and it ends up making the whole sphere black with orange lines emitting from the texture around the sphere, looks like North South East West lines.
Probably due to texture clamping. Wherever the orange circle touches the outside row/column of pixels, that final outside edge gets repeated for every texel beyond the texture area.
Inset the circle in your texture so it has a row of black (or transparent) pixels all around the outside of the image, and the extra lines should disappear.
I opened up the shader file for the projector and deleted the line //Offset -1, -1
It cleared up all the black lines for me. Hope that helps someone.