What do you do when caught in the middle?

I read this article yesterday about a professor applying for a job as department chair at a university. He tells of meeting the Dean who made it quite clear that there were a lot of problems with the department and he wanted someone to come in who was willing to "shake up the place and get rid of some of the deadwood." He then met with the faculty, some of whom were among the ones the Dean wanted to see cut loose, who were looking for someone to come in who would "be on the their side" against the administration.

This job applicant realized immediately that the person to whom he would be responsible if hired had opposite expectations from those immediately empowered to hire him. What did he choose to do? He returned home and withdrew his application!

For some people it isn't that easy; they are already in the position of trying to please two groups with competing interests. In fact, I'm sure that it is quite common in today's organizations. What is the right thing to do in these situations? As an aspiring servant-leader, how does one move forward?