Jacobsen, I think you need to do some more research in how accreditation works. The regional accreditation bodies do not just "willy-nilly" hand out their accreditation to any and all who apply and write them a check. Secondly these agencies are not of the government but instead private non-profits, thus have no "jurisdiction" in the legal sense of the word (just to clarify for those who may read this later). However if a school has a corporate structure which would allow them to use accreditation from one location elsewhere in the country it is assumed the accrediting body is aware of this and by default approves or in the worst case scenario, at least doesn't mind.
The AACSB is truly a voluntary and redundant accreditation. Nice to have, but not necessary. The AACSB also has competition with the ACBSP and even the much less well known (but CHEA recognized) IACBE.
Also as business schools are expected to understand business in the sense of benefit > risk + expense, it would only make sense for a school to do some form of market research to see if the increased expense and hassle of obtaining a redundant business specific accreditation for their "B" school is worthwhile or a sound investment.
Lastly the AACSB/ACBSP/IACBE are business specific. They do not accredit the whole school in the sense that the NCA or SACS does. You're apparently confused as to the scope and purpose of this type of accreditation.
Not having this program specific accreditation does not equate a regionally accredited school with a diploma mill either. In fact having no accreditation does not inherently make a school a diploma mill but that’s a different conversation altogether.
Any questions?