No, but they should. If you were interviewing someone to fill a nursing position, you'd ask medical questions, wouldn't you?

I was helping to interview someone to cover a weekend support position, and we simply needed someone with enough SQL knowledge that if a job stopped (such as replication) he could restart it. Anything more than that, his job was to call someone else.

So here was the question I asked the 3 people that interviewed for the position: "If you're the only one around and a web developer is working on the weekend, and he asks you to give him permissions to run SQL Profiler in production so that he can trap an error hitting the live website, what is your response?"

The answer I liked best was by the first interviewer, "I don't know what SQL Profiler does or what impact it would have on production, so no, I won't. You'll need to talk to the dba about that when he's here."