As I understand it and have seen it work on my system, when you download a book via overdrive, you don't actually get the book (epub file) itslef. You get a "stub" file with an extension ".acsm". You then open that file in ADE and it does the actual download of the epub file. So you need ADE or you cannot get the real epub file. I do not know of anyway around this. it is all about DRM and security, I assume.
There are ways of removing the DRM after you have the epub on your harddrive. You can do some searches and find out info about that.