There is always a small degree of cross-knowledge needed for those areas where support overlaps. Linux specialists would need some Windows knowledge to set up Samba access, for example. And most desktops are Windows, so everyone knows the basics there.
However most SA and DBA teams I've known are split up into specialist subteams; Linux v. Solaris v. AIX (though there are similarities) and especially v. Windows, and Sybase v. Oracle v. SQL. There don't seem to be any generalists or polymaths.
Myself, supporting distributed workload automation, I must know multiple OSes and databases, shell and bat scripting, basic networking, Boolean logic, ESP (knowing what the user really needs instead of what s/he's saying) and diplomacy (The art of gently telling someone the problem is their fault on an open conference call).
