Mix Transparency Render Layer with pure White Backround picture still slightly grey


I have a problem I stumbled upon in a bigger project. I want to have a pure white background in my image. So I rendered the main Render Layer with transparency enabled and added a pure white background with a mix node. After saving the image and opening in photohshop the background in the image is slightly grey (like 13%).

Im using cycles Render and the filmic color-Management. I also tried the alpha over node or mixing with a white image with the same outcome.

As i have this problem after compositing I think it has nothing to do with my lights. I hope somebody can help me.

I made a startup scene with the settings i am using and will attach it here: https://www.dropbox.com/s/azz2j3nez2z5x27/GreyColorProblem.blend?dl=0

Not looked at your .blend.

I think your problem is with using Filmic… with Flimic, R=1, G=1, B=1 is no longer white. The easiest solution is to ramp up your background colour to R=2, G=2, B=2.