System Information
Windows 10 - nvidia geforce gtx 770m

Blender Version
Broken: 2.78 e12f5b6
Worked: (2.77)

I was currently exporting fbx meshes in 2.77 but now in 2.78 the export seems to be broken, not sure if is happening with the other export options. The current settings are the ones in the attached images. I also attached an example of what is happening. The fbx exporter is making the normal map to be cloned to the others textures slots ass a diffuse influence. That is an idea of what I think is happening.

Exact steps for others to reproduce the error
Open Blender > select object (that already has UV), add material > Diffuse color = full white, intensity 1.000, Specular Color = full black, intensity 1.000 (after the diffuse color and specular color I did not touch anything else in the material tab. Move to texture tab > add 2 textures, diffuse and normal, in diffuse I leave it alone with the influence in color and the normal I only touch (image sampling normal map check box) and in influence disable color and check Normal. After that I just export the mesh as fbx with the following settings: [Main tab] Selected only (disable Empty, Camera, Lamp, Armature and Other (leave Mesh on). Path mode via copy and embed textures, Geometry. [Geometries] Appy modifiers, [Armatures] Disable add leaf bone, [Animation] uncheck baked animation.

UPDATE : october - 11 - 2016 (updated blendFile with packed files and fbx after doing the export again in a clean install of blender 2.77a) Even if I copy the mesh from 2.78 to 2.77a it makes the same problem once I export from 2.77a... it seems to be something in the data of the object itself... it also happens to all the blender files I use to have with 2.78, notice that I removed all the addons before export.

BlendFile Attached.

FBX attached.