The right to change ownership of a file is restricted to root. The owning group of a file can only be changed by users that are members of both groups: The one which owns it and the one that shall own it.
I think these rules make sense, since like it is, no-one can create a file 'myoppinionabouttheboss.txt' and secretly 'donate' it to somebody else, or a group that he has no access to.
stw@laptop:~> grep stw /etc/group uucp:x:14:stw dialout:x:16:stw audio:x:17:stw video:x:33:stw stw@laptop:~> touch file stw@laptop:~> ls -l file -rw-r--r-- 1 stw users 0 2004-05-17 11:53 file stw@laptop:~> chgrp uucp file stw@laptop:~> ls -l file -rw-r--r-- 1 stw uucp 0 2004-05-17 11:53 file stw@laptop:~> chown :audio file stw@laptop:~> ls -l file -rw-r--r-- 1 stw audio 0 2004-05-17 11:53 file stw@laptop:~> chown :root file chown: Ändern der Gruppe für „file“: Die Operation ist nicht erlaubt stw@laptop:~> LANG=C chown :root file chown: changing group of 'file': Operation not permitted stw@laptop:~> rm file