Short answer: if you could point to any leading business school that would, on principle, not recruit someone with an MSc in engineering then perhaps you would have a point. However, I don't think that's the case.
Long answer: I'm a final-year PhD candidate at the University of Edinburgh. I have an undergrad in theology and a masters in informatics. The issue isn't the discipline of your degree, but whether it seems that you are the sort of person who could complete a good PhD at the school in question. What really matter are variables like: are you a dilligent student; is the school able to supervise the topic you want to research; do you have an idea of what you want to research which in some way sounds like a viable PhD; do you have an idea of the current literature; and so on. The average MBA does not prepare students for these questions any more than an MEng, because neither typically involved original research or critical engagement with current journals. My business school has several MEng students as PhD students and alumni. I don't think that's very unusual.
Long answer: I'm a final-year PhD candidate at the University of Edinburgh. I have an undergrad in theology and a masters in informatics. The issue isn't the discipline of your degree, but whether it seems that you are the sort of person who could complete a good PhD at the school in question. What really matter are variables like: are you a dilligent student; is the school able to supervise the topic you want to research; do you have an idea of what you want to research which in some way sounds like a viable PhD; do you have an idea of the current literature; and so on. The average MBA does not prepare students for these questions any more than an MEng, because neither typically involved original research or critical engagement with current journals. My business school has several MEng students as PhD students and alumni. I don't think that's very unusual.