I for one think that Michael Winerip's story about the removal of a popular and successful principal in Burlington, Vermont in order to qualify for federal stimulus money gets an important story right. I don't think this can be quantified, especially while we're in the middle of the process, but I've heard plenty of similar anecdotes. You could start with Central Falls, where nobody seemed to blame the principal, who was moved to middle school principal (iirc), and the previous AP moved up. Not moves consistent with a bad school administration.
This isn't 1992. The "lowest-performing schools" have been under a microscope for a decade.
In the Providence high schools effected, you have one that went downhill after the school's founding principal was moved to run a high school turnaround three years ago. The low-performing school has been merged with another small school run by a principal who has managed to more or less maintain the moderately good scores at her current school. And you have another principal who raised reading scores over 40% in two years before being faced with demotion to AP or firing.
I would guess that in about half of these cases removing the principal doesn't make sense, because there is no significantly better alternative at hand, but nobody really knows.