While it's true that protecting your computer accounts with a password will help prevent someone from logging in to your PC and using your operating environment without your knowledge, this alone will not prevent others from accessing your files when you are offline. As you recall, Linux Mint features a live CD that includes a fully usable operating environment, complete with a web browser and file manager. In fact, most Linux distributions feature live CDs nowadays, which are useful for much more than just booting an operating environment.
With a live CD, you can directly access the underlying hard drive of the computer, regardless of the operating system installed on it. Even if your user account is password protected, a live CD would bypass all the permissions on the underlying filesystem and allow the files to be freely viewed. This means that if your computer were to ever get stolen or fall into the wrong hands, your files would be easily accessible to anyone...
