What you are experiencing is the major reason that ULS was deprecated. All Access databases in A2003 and earlier are secured. You are just not aware of it because unless you have created a custom work group and logged into it, Access just uses the default System.mdw and logs you into that as an Admin.
If you created a workgroup with a name other than System.mdw, your System.mdw will still be unaltered so you can just rejoin it and all databases will appear to be unsecured again. If you modified System.mdw, you will need to locate a clean copy so you can join it. I have attached a clean copy you can use.
In the future, if you have to work with a database secured with ULS, create a shortcut and add /wrkgrp workgroupname.mdw as parameters. If you join a workgroup, Access updates the registry with that information and that is why all subsequent applications appear to be secured (they aren't really). You are still connected to the secured workgroup until you join another. Once you join the clean workgroup I sent, that will update your registry and you will be fine. When you use the /wrkgrp runtime argument, the registry is not updated so other databases don't act like they are secured when they are not.
This is the Access Security FAQ. http://support.microsoft.com/kb/207793
It will explain in more detail what I summarized here and it will tell you how to correctly secure a database should you want to.