A survey of the journals whose stories have been consistently selected for The Best American Short Stories and the O. Henry Prize Stories includes The New Yorker, Glimmer Train, Harper's Magazine, Ecotone, The Paris Review, Ploughshares, Granta, The Kenyon Review, and The Iowa Review, among others. Several of these publications are run by universities, and the editorial staffs of these journals include academic writing teachers and students. I think whether these editors do it consciously or not, they must have some tendency to lean toward writers coming out of academia, simply because that's what they've learned is representative of quality writing. As an academic scientist, I can attest to picking up biases when evaluating the work of other scientists for publication. Simply put, I'm trained one way, so I'm going to rely on those lessons when judging the work of others. The other part of this discussion involves the cover letter that accompanies a short story submission. If covers letters matter to an editor, then degrees, just like publications, will probably impress them.
Luckily, exceptions to this rule are plentiful. Jennifer mentioned Alice Munro, a regular in The New Yorker, who never got her MFA. From the editorial side of things, some prestigious journals still look at submissions blind, meaning the cover letters and the writer's identity is removed before a story is judged.
The second part of this question was whether or not there is an "MFA-type" story. I'll start by saying that, while I have taken a few university writing and literature classes, I do not have an MFA, so I can't completely discuss this topic from my own experience. But, I do believe that academia promotes a more uniform style than would be around if every writer had to develop on their own. Again, techniques and philosophies are shared since that's the nature of education, so I think it's normal that writers coming from the same place risk sounding the same.
Is this a good thing for literature? Probably not. But, I think education is good, and if a writer is attempting to learn writing from others, uniformity may be impossible to avoid. Just as with the rules and preferences we discuss in our blogs, the writer is faced with the task of learning the rules and then daring to break them for the better. That second step is crucial, in my opinion. Without it, I don't believe any writer can be great.