I'm sorry, could you post a full res version of that?  I'm really not familiar with the "Simple" view, and none of the text is exactly readable.  That said, if I'm reading it right, your transparency is at 1, but your falloff is at 0.6.  And you seem to have a highlight?  If you want something to be invisible, it should have no highlight, no reflection, and no falloff in addition to being fully transparent.  Falloff is meant to mimic the way weaves like nylon become less transparent.  It's not useful in general, because that's better handled with EdgeBlend. 

Still, I don't see from this why a texture would be necessary.  Diffuse color has nothing to do with transparency.  If you just want a plain, flat red, or even a red with a little noise to it, a texture is a waste of resources.  To render, textures have to be made into fully uncompressed files.  They get dumped into a temp folder that doesn't seem to get cleaned much.  They can be from about 10 to over 100 MB.   Unnecessary textures can waste more resources than a mesh with millions of polys.