When I invert the colors in Blender, I don't get the same result at all as Photoshop. The middle-grey background should not change, but it gets brighter in Blender while it stay the same value in Photoshop.
Blender will generally linearize colors when importing 8bit images. Photoshop does not. Normally, Blender's behavior is correct but in this case you are encoding data here, not colors. You can inform Blender of this and disable the de-gamma step by setting your input color space to "linear" or "raw" instead of "sRGB".