In 19 years (7 of them as consultant) of working with SQL, I think only once did I only do one part of what many describes as a DBA (and that was at one of the top 5 banks by size). In most places, where my title has ranged from Client Servers Applications Specialist (this was when most companies where just introducing SQL 6/6.5) to Senior SQL Database Architect, I have mostly been "the SQL guy", if it had anything to do with SQL, it was my responsibility to get it done (or to find the right consultants to get it done if I did not have the needed experience).

As some have said, titles are pretty meaningless. Maybe in larger organizations they make some sense just to make sure people know who is in charge....

The job today is a magnitude harder in some respects (i.e. much wider experience needed), but also a LOT easier in some ways (disk management, oh what a joy that was in 6 and 6.5, and 4.21 but I luckily just had a few months of exposure to it).