I will not look up to CMU profile. I only look up to Baruch profile.
Well The reason I posted the link is not to show CMU profile but to answer your question
">> Can you show your data to support your claim? "
I thought about where do I get data on people heading various departments and their background. One place to find such data is a page listing people giving presentations at schools (most of them are heads of departments). And one school that came to mind was CMU, they post profiles of the speakers giving presentations. That page has nothing to do with CMU directly except for listing people who spoke there once or twice. But it has information on what backgrounds people have, so you can check for yourself that there are department heads with PhDs.
And again, I'm not claiming that ALL PhDs are doing better job than MBAs, I'm saying that SOME PhDs are doing better job than MBAs.