When I was an intern, I actually talked to the press a couple times. We had no set official policy, at least not that I was aware of. Typically, in practice, whoever was the lead on a project would talk to the media about that project.
One of the times, I had a very positive experience with the press where I talked up an event we had put together (where I was the lead person) and got a really great article out of it...front page of the community section with a big positive quote. The local reporter assigned to us had a pretty good working relationship with us and so that helped. This was also a regional paper that covered the whole county, so it was good exposure.
However, I got burned one time by a reporter for the local weekly paper that covered just the town. He asked me some questions about a park which I had assumed was in relation to the long-range parks plan I was putting together. As it turns out, short-range plans for that park were already drawing controversy (which I had not known much about) and he interpreted my information about the long-range plan as being more short-term stuff to add to the controversy. This was one of those situations where I should have forwarded it to the department head, as he was leading the short-term stuff for that park, but unfortuately I didn't know of those plans. I think the reporter definitely tricked me, because the other questions of his were clearly about the broad long-range plan, and not about the imminent plans for this specific park. After that, I tried to avoid him as much as possible and direct any inquiries to my supervisor.
"Life's a journey, not a destination"