As a candidate, you can't control the selection process but you should weigh committee membership in your evaluation of the institution. Few faculty members, students, or staff members have any idea about how university administrators spend their days. The result is a series of questions designed to ascertain personality rather than the abilities and leadership talents required for success in the specific post. If it obviously does not, beware. Questions about how you would handle disputes with other leaders may cloak a desire for a fighter to fend off this or that vice-president or dean, or often, the president.
Hypothetical scenarios are apt to be true.
Avoid any campus that appears to see administration as guerrilla warfare and that has search-committee members who see you as a potential ally or enemy in a war you know nothing about. I have been amazed at how much dirt is revealed over a day or two on campus. People can't seem to resist telling a total stranger who is interested in the possibility of holding a leadership position on that campus of every scandal, suspicion, rumor and alleged misdeed of the central administration. When conducting interviews of prospective administrators on my own campus, I have been surprised by the number of unpleasant rumors that I have been asked to comment upon. It took me a while to realize that those ingenuous or devious enough to pass on scandalous rumors actually are, in their mind, currying favor with a potential new power holder.