Correction of correction, the readonly thing turns out to be an issue in the latest version of Unity, to which there is a workaround too.. so using unticking embedded textures is now a workable solution for me. Cheers

Correction, doing it this way (non-embedded) creates a more severe problem for me (in Unity) whereby the imported Materials are read-only (not decompressed within Unity), so the usual mess-ups that happen between CC3 and Unity (namely, opacity, which is always imported incorrectly in Unity) cannot be fixed. So it is looking like I will need to, manually, one by one, recreate every material for my character...

so yes.. please address this issue...

I am having the same problem, and it only started recently. Last time I tried to export this worked perfectly, but today, I am not getting any textures exported to the FBX.

@Feedback Tracker Admin: I think you are misunderstanding the problem. Textures can be exported to separate files (by unticking embed), this works, but they should be able to be exported inside of the FBX file. Used to be all I needed was the FBX file, I could import it (in my case, into Unity) and all the textures would be available (in my case, Unity decompresses them into a .fbm folder, same way it appears when exported externally), but now, this glitch seems to have occured for me, where all the textures are missing, and my character is entirely grey, and even though the materials are found in the fbx, the textures for them are not, the materials simply use a solid grey albedo. 

That said, luckily (in my case) copying the exported fbm folder over alongside the fbx file to Unity, is allowing it to find and link up those textures no problem. But this is still a bug that needs fixing, as embedded textures are no longer working, and they used to.