This is a very popular phrase that circles around the HR and management community a lot...and in fact has been doing so even during the time I was a recruiter some 25+ years ago. And, in all that time has consistently proven to be true.
However, I'd like to frame this truth in a different way. People don't leave jobs, they leave relationships. Because, in essence, that's what we're talking about. Leaving anyone, boss or not, is leaving a relationship.