If you can get a Masters in English, you can probably get a Masters from a divinity school.
The Doctor of Ministry degree sounds like a Doctor of Education degree, meaning you don't actually have to know something. You have to write about how to teach it (or in this case, preach it).
I doubt that divinity schools had MAs in “Islamic studies” 30 years ago. But it is possible.
Caution is required because bloggers like to make up stuff about Obama associates when the reality is plenty alarming enough.