The default ambient parameters of camera and grid are not same, the former is less accurate than the latter, this is because the rendered camera image is mainly used in viewing than grid.
For example:
Camera: -ab 2, -aa 0.2, -ad 400, -ar 15, -as 64
Grid: -ab 8 -aa 0.1, -ad 512, -ar 32, -as 256
So, Grid result is more accurate than camera.
Another possible reason is: the objective material must be fully diffuse, if not, results of camera and grid are not same in theory.