That's revisionist history.
Atlanta didn't intentionally move away from Rex. All signs were pointing that he was the leading candidate, but when Blank's mother passed away, they put all negotiations on hold, which miffed Ryan. That's when the Bills offered him the job and he didn't want to wait a day or two to hear back from Atlanta. That's the likely genesis of the "don't let him out of the building" quote, because Bills knew that Atlanta was likely his top choice.
In retrospect, the timing of Blank's mother's death killed the Bills in the last two years.