It seems that this password system protects only the stored passwords, not the contents of the account mailboxes as well.

Passwords Thunderbird can remember are your account passwords. They are needed to access your account on the server. They are not needed to access the (local) profile.

You can set a master password to protect the account passwords. http://kb.mozillazine.org/Master_password

Check this article for more information on how to protect the profile. http://kb.mozillazine.org/Protect_the_profiles_contents

NMB1 said

Supposedly, once a user is logged into TB using the password, it is only needed again to access the stored passwords (via Tools\Options\Security). BUT I FOUND -- when the initial TB login dialog appears, if you click Cancel instead of giving the password, you are immediately given access to the account (set at the mailbox from which you last exited TB). Then, if you want to access another mailbox, you need only click on Cancel to be given access.This is clearly a security bug -- the password isn't needed to access emails! However, if you do log in to TB using the password instead of clicking Cancel, the subsequent dialog boxes do not appear. It seems that this password system protects only the stored passwords, not the contents of the account mailboxes as well..

Got it now.

Thanks, John99 and Christ1, for your help

NMB1