Can someone harm my computer just using grub?

Solution 1:

Yes they can; by editing GRUB to boot to single user mode.

They can then reset the root password simply by entering passwd. It is then possible to for the attacker to mount file systems and basically, do as they please...

This guide provides you with information on locking the GRUB command-prompt with a password: https://help.ubuntu.com/community/Grub2/Passwords

Solution 2:

DevRobot's answer is the correct answer for the question being asked. I wanted to make you aware (if you weren't already) that grub is probably not what you should worry most about...

Physical access is total access (for the most part). Your OS passwords are meaningless if someone throws a flash drive in your computer and boots from it. They don't even need to change your root password - they have their own and can suddenly access all the files on your hard disk. If you're more worried about uptime and stability, then that same person could format your hard disk or make any changes whatsoever from the flash drive that you could do physically logged in.

The best value physical security is just to encrypt your hard disk. You won't notice a difference, but access without the disk password is essentially impossible.