I would argue that the Performance Tester/Engineer and the DBA should do it together. If you are asking who should be "in-charge", I really don't know. I really try not to pay much attention to hierarchy (maybe that is why I don't do a lot of government work...hmmmm)
I think the two of you developing, executing, and analyzing the tests together will have more success than either of you will alone.
Depending on your configuration, volume testing may be testing more than just the application. Some system level/enterprise testing I am aware of turned up some major supporting software problems while doing some load/volume testing. If you are in any kind of a LAN or network environment "little" things like firewalls, DB Servers etc, get involved.
With us, volume testing is definitely about the data. We sometimes use our load tool (LoadRunner) for that but other times we just use custom tools that basically shove data back and forth from a database via a slew of queries running from different machines or we use certain types of batch processes. (Sometimes our load tool is used during this just to simulate a background load. We then check response times in the tool.) For how we plan this out, we just look at what areas of our system data passes through and what areas are specifically "bulk data" related -- in other words, where we need a lot of data to be going through the pipe.