The live versions of Linux that you boot from a CD or a USB stick should not touch anything on your hard disk. However, most of them will allow you to mount and or run fdisk on your hard disk, and with these tools you can make changes, and you can hose your disk.
If you boot from a live distro and run firefox say, that is perfectly safe.
If you boot from a live distro and run fdisk on the hdd and do more than look, or mount any of the filesystems RW and make changes, sure you can render the machine unbootable.
By the same token, the live distros are very handy for being able to mount the hdd on a problematic system and allow you to make repairs. The knife cuts both ways.