I expect that, if given the title Director, the candidate has a P&L and makes a significant part of her income through making the P&L. Director should be "Manager of Managers" -- close to "Vice President"
But now imagine I'm full of myself with my new "Director" title, and go out to interview for real director-level jobs. Man, the previous company would have done me no favors as I go out there and get absolutely slaughtered in interviews.