The former PD of my fellowship had an MBA. The guy now heads one of the largest hospitals in the local tri-state region, previously was the chief clinical officer at the Lindner Center (a private psychiatric center in the Cincinnati area, and considered a top private clinic), and used to be the chief forensic officer at the place I currently work.
You could do incredible things with an MBA, but you also got to have the drive to push yourself to do it. They just won't come to you. The PD I mentioned is one of the best doctors I know, and it's not just his MBA, but his charisma, leadership, friendliness, clinical skills, and hard work that got him to where he is. Even as a "regular" psychiatrist, the guy was winning national level awards for his quality of work in several areas such as teaching.
As for my fellowship, it was a loss to see him leave as PD, but we got one of the best forensic psychiatrists (and ranked one of the top physicians in the country) to take his place who also happened to be a good teacher in addition to having impressive credentials.