I installed Debian on this new laptop Asus x50gl.
Debian will not boot into a GUI, it will only start with black screen, console mode.
GDM is running, dpkg-reconfigure doesn't solve the problem. Can't get X to run. The laptop has an nvidia graphics card.

So, I installed Ubuntu. It works, well. They are nearly the same. So I thought, mount Debian, compare the xorg.confs, gdm.conf, etc, maybe I can get Debian going.

My question is: is it not a security breach if I can mount Debian, change things, save the changes, basically do what I want with what should be a separate system? Not that I have anything to hide, just out of principle.

It's not a breach, because you are doing it to your own system. It would be a breach if someone else would do that - either by remotely accessing your Ubuntu (and gaining elevated privileges) or by having physical access to your box. In both of those cases, the actual breach isn't the mounting of the Debian partition, but rather the gaining of the ability to do so. What you have described is totally normal and expected behavior. It's the same principle used by rescue CDs (you mount any disk partitions you wish to work with). In fact, you could have done what you did by simply using the Ubuntu CD's live environment - without actually having to install Ubuntu.

If, rather than 'breach' you mean 'risk', then yes it is. If, for example, you left your laptop on the train, as seems to be in accordance with Government guidelines here, then someone could put in a Live CD. What happens then depends on stuff like bios options and encryption, but you should certainly think about the risk.