Part of my education ensured I got a decent understanding of how Databases work. I went into the field expecting to do database work, and a lot of it. I'm a web app guy; it comes with the territory I guess.
My two jobs as a developer have been at two shops that would best be described as tiny (2 people myself included, and then just me) and tiny (3 developers, briefly having a fourth). I have not observed an immediate business need for, nor worked anywhere that had the resources to employ a dedicated DB guy. I can envision some scenarios where that would change (including a new job :P).
As to the rest, I agree that abstraction is also a factor and as developers we're way up on top/outside looking in. I can't imagine doing web app development without DB skills, and I consider Sql/DB Management to be both an important tool and an area I need to stay sharp in.
I'll add that I treat the database side as its own field. There's skills that translate between the two, but there's a lot of specialized knowledge I need to acquire to get better at it, and that being a good programmer doesn't necessarily mean I'm doing a good job on the back end either (fortunately, I'm not a good programmer ;) ). Also, I'm pretty sure that's what she said.