To answer your question from where I stand...it is way to complex to sum it up easily. If you site has a basis that is primarily jokes and funny images your relationship is going to be different than if your forum is the communication center for a product or service you offer and whatever millions of other possibilities stand in between those two.In your opinion what sort of relationship should forum admin have with forum members, and how important is that ?
For instance...say you had a forum that was a group support place for people dealing with terminal illness...well that is not the place you want a robotic persona talking to people constantly. People who are somewhere trying to open up and reach out don't want to get an answering machine. Then again I belong to forums that you can beat the members with a club and they will post something they are told to not post ...immediately following the post from staff telling them not to specifically. It is all about what is appropriate for your arena.
This is another one of those things that you just have to assess the situation and make a decision for yourself if it is your site. If it is not, then it must be accepted that things run the way they do at a given place for a reason that was determined by the people who run the place and can see more of the complete picture and you just have to let the admins do their job.
So yeah, my answer is there is no one right answer...because than you would have to define a wrong answer.... and with an infinite possibilities of sites you could create, you could also create an infinite amount of predictable and unforeseeable circumstances that could change the answer.