My 12.10 computer has several accounts on it. My wife has a Kindle Keyboard 3G that she manages with Calibre. The problem is that every time she tries to eject the device in Calibre if asks for my password. Mine is the main administrative account which may be why it wants my password.
I'm not at the computer so am not positive whether I could eject from the file manager without a password, though I know that other USB flash drives don't require it.
Does this occur if you mount the Kindle 3 (3G), when Calibre is not running?
There are multiple known issues with conflict between Nautilus/OS and Calibre over mount/unmount. Also, some efforts to address this (eg. calibre-mount-helper) introduced security flaws, and are not recommended.
The likely best fix is to use the latest Calibre version, from: http://calibre-ebook.com/