Since the tone of your post shows that you don't believe me, I'll past Stanford's response to your question:
Do I have to work for one of the top five companies in my field in order to be a competitive candidate for admission to the Stanford MBA Program?
We make a concerted effort to attract and admit students from a broad range of professional backgrounds and experiences. Therefore, there are no particular industries or sets of companies that put an applicant at a competitive advantage in the admission process. Although investment banks and management consulting firms are represented at Stanford, we also draw students from non-profit organizations, multi-national corporations, family businesses, entrepreneurial ventures, and the public sector.
As you approach your MBA application, keep in mind that we are more interested in the impact you have had in your work place than the name or stature of your organization. Have you made the most of your professional opportunities? Are you cultivating your leadership and team skills and making a difference? In the end, don't build your resume simply to be an attractive business school applicant, but rather seek opportunities that are truly challenging and rewarding for your own professional and personal growth.
And yes all of the career types that you pointed to can get an MBA. One of my most impressive study group members was a middle school teacher before HBS. Not trying to plug our book too much, but your skepticism leads me to believe that you would benefit greatly from its insights!