No, they don't hire their boss. But their input is (nearly always) invited in the process.
Have you ever been part of a search for a department chair, a dean, or a president at a university? In most cases, there is a search committee, and at the higher levels a headhunting firm is frequently hired to thin the herd of applicants. When the finalists have been determined, anywhere from 3-5 are brought to campus. The campus visits generally include closed interviews with key faculty member groups (faculty senate) and administrators for the higher level candidates (presidents, veeps, deans), and frequently include separate P&S meets for deans, and staff and grad student meets for department chair candidates. Then there are open forums where the candidate will present their vision, their goals, and their past successes to any who want to attend. Depending on how big the audience is, those can also include Q&A sessions. Following each candidate's visit, surveys are provided to those involved (they're often links to online surveys now that are emailed out) and those results are tallied.
Look at the results of the surveys above. That input was REQUESTED, and was clearly IGNORED. If someone asked for your opinions, and your responses were like above, and they went the completely opposite direction, would you be happy about it? Or is it just acceptable to you (and others) because it's a university, and more specifically it's the University of Iowa, and even MORE specifically it's those elitist, liberal academics in Iowa City?