I think I never really used the "Crop" option for the "Fullscreen in browser" setting before. Now that I have need of it, I noticed that objects on layers with a "Parallax" setting of 0,0 get displaced.
To test this you can simply open the top-down shooter template in Construct 2. The project does have a text object on a non-scrolling layer placed in the top left corner. It does display fine in all fullscreen modes (apart from what you expect to happen when using Scale inner/outer) but "Crop". The text will not show at the top left corner anymore, but appear displaced inside the game area.
This appears to be a glitch to me.