I am also sure the study will show Donald Trump, Rupert Murdoch and Mark Zuckerberg run orgs with highly competent managers. But it is not competence in my book.
My issue is mindless ambition/win at all costs/do whatever it takes produces "competence" too.
The more data that pours in, the more we will realizes that stuff needs to be filtered out from our definitions of competence. The costs are too great imho.