Take a look in the External References Palette. Highlight an existing reference and take a look under Details section at the bottom.
Found path shows where the current referenced file is located.
If you edit this path it jumps back to the full path leading you to believe that you cannot change the path from fixed to relative.
Pay closer attention and try it again. Edit the path in the Found Path field. Now look in the Saved Path just above the found path. The Saved Path stores what you edited in the Found Path field.