Turning down a 2nd interview is essentially turning down the job. Especially since at the time he was going to stay in a lesser position with the Browns and since Miami offered that job to everyone possible. You can play semantics all you want but he turned the job down when he turned down that 2nd interview
Unless you're willing to say that every 2nd interview equals a job offer, then Farmer didn't turn down a job offer, he turned down a 2nd interview. By turning down that 2nd interview, Farmer certainly signaled his intentions that he
would have turned down a job offer, had Miami made one, but
Miami didn't make the job offer. That isn't semantics, it's specifics.