But lo and behold, the Finder can *ignore* permissions! Select your volume, File -> Show_Info, and click 'Ignore privileges on this volume' in the Privileges section. Presto, you can now read and write other people's files on that volume!
Check out the original Knowledge Base article (106604) for more details...
[Editor's note: Also see this hint, which discusses how the Ignore Privileges flag is used with removable drives.]

