Not just the Bengals. Word out of Pittsburgh is that their owner fired the O coordinator without the head coach's blessing:
http://profootballtalk.nbcsports.com...-for-a-change/Although the official company line on the departure of Steelers offensive coordinator Bruce Arians is that he retired, it’s been widely reported that he was actually forced out by Steelers owner Art Rooney II. In an interview on the team’s web site, Rooney declined to get into specifics, but didn’t deny that he’s the reason Arians is out.
It's not just Cincinnati. The owners do call the shots on things like the hiring of coaches