Doctor Who 2 (7/9/2012)
Bottom line: if the agency is small enough, they don't want a DBA. They're not willing to pay that "DBA tax". They'll make anyone who has any IT experience be the developer, administrator, PC tech, help desk, network engineer and of course DBA.
I'm not sure you're getting the same point I wanted to make. It isn't that you need a DBA, or that a DBA is a tax. It's that the DBA is often seen as a tax for a system, not providing value, but just cost. That could apply to any position.
The idea is that you want to prove you have value to the company, whatever your position. Make sure they see you as valuable, or I would advise you move on.
Side note: I wouldn't make my life/career decisions based on the impact to other employees. You can talk with them, but if you don't like the work, move on. Life is short, way too short to stick around if you don't have to in a position that doesn't work for you.