there is no right answer and it's all CYA

where i work DBA's always took care of the SQL servers down to doing windows updates and installing windows, sql, etc. but that is only because there has always been at least one DBA that has come from a server background

other companies the DBA's do strictly SQL and others the housekeeping tasks on the hardware

the issue here is that one group doesn't want to be held responsible in case something goes wrong. say a backup fails and the data needs to be restored then and there. server people don't want the dba's to say that their tape drive or whatever failed.

for backups we used to share a tape robot, but management was separated where DBA's tracked SQL backups and blank tapes. it was OK, but everyone would steal tapes from each other from time to time. now the server people do disk backups on Evault and us SQL people are about to get our own Evault server for backups and the tape robot is now 90% SQL