In our environment we are mostly production DBA's, but we are production DBA's on 90% purchased/vendor applications; as such we spend a significant amount of time troubleshooting and rolling out new versions of codes for bug fixes, etc in response to problem tickets from the business users - I do not consider this self-directed.

Part of our problem may be our staffing - we have 2 FTE's and a (new) full-time contractor managing 120 instances over 110 servers, including 12 two-node and three-node clusters; we support over 1000 databases among us. To me this has always seemed like too much per DBA such that we spend most of our time rushing from problem to problem with the duct tape at the ready.

I agree with Steve's original premise that a lot of time for an established production DBA should be self-directed, but I also agree with the few previous posters that point out that businesses usually don't recognize the value in that - mine definitely doesn't.