Thanks for the suggestion; this was somewhat helpful. I ran the file command on several disk images in my downloads directory on OS X. The results: two of them said they were "lif file" and others were identified as "data," even though the file extension of all is ".dmg" Disk image files of both kinds were able to mount.

The problematic file which did not mount was also identified as a "lif file" but Disk Copy (which is supposed to mount the image) complains there are no mountable file systems.

Perhaps it is the result of the sharing parties inability to make available a valid disk image?