Avoid Texture Symmetry on complex Uv maps In Blender2.79, texture paint is showing symmetry even after activating these settings-  

Mirror modifier - Applied
Texture Symmetry = Off
Sculpt Symmetry = Off

One explanation can be found here UVs overlap causing texture symmetry  

However,in this case there is clearly  no Uv overlap as seen in the video below .
How to avoid texture symmetry on complex Uv maps?
Eventhough the Mirror modifier was applied ,it was applied after the Uv's were unwrapped causing Symmetry (even if the Texture paint symmetry options were off).Applying the mirror modifier and unwrapping Uv's after, solved the issue. 

Thanks to @Craig D Jones for pointing it out.