Sound like you got bad advice from support - there is no support for backup from within Adobe Digital Editions. To back up the files you need to back up the .pdf and .epub files that are normally in the My Document folder under My Digital Edtions ( Document and Digital Editions folder on the mac).
To determine the actual location of a particular file, Inside of ADE you can select a book and press Ctrl (Cmd on Mac) - i to bring up the "More Info" dialog which will display the full path to the file.
However the most important thing that you can do to back up your books is to make sure you have authorized with an AdobeID. If you are activated anonymously then backing up the book files won't help because you will not be able to access them if your computer get signficantly change (OS upgrade etc...), since they are tied to the activations on that machine. To check to see that you are authorized with an AdobeID, select "Authorize Computer..." from the 'Library' menu.