I received my last PhD from the Atlantic International University.  I also attended Boucher Insitute for Naturopathic Medicine for two years.  I was recently asked if they were an accredited university.

The following is taken from the AIU website: 

Atlantic International University is accredited by the Accreditation Service for International Schools, Colleges and Universities (ASIC). ASIC Accreditation is an internationally renowned quality standard for colleges and universities. Visit ASIC’s Directory of Accredited Colleges and Universities. ASIC is a member of CHEA International Quality Group (CIQG) in the USA, an approved accreditation body by the Ministerial Department of the Home Office in the UK, and is listed in the International Directory of the Council for Higher Education Accreditation (CHEA). AIU meets all state and federal laws as a degree-granting institution in the United States and the State of Hawaii. The University was legally established by corporate charter in 1998 and is in good standing.

It has the right to offer BA, MA & PhD programs and degrees.

The following was taken form Boucher Institute of Naturopathic Medicine (I only attended the first two years) website:

Accreditation

 Accreditation is recognition granted to educational institutions, or to specialized and professional programs offered by educational institutions, signifying attainment of a certain specified level of quality and integrity in its operations. This recognition entitles programs and institutions to the confidence of the general public, the educational community, governmental agencies and other agencies and organizations. 

Council on Naturopathic Medical Education, Handbook of Accreditation, 2007 Edition

The difference is that Boucher is only recognized within the confines of North American Naturopathic Association & the Private Career Training Institutions Agency (PCTIA) of British Columbia; and can only offer a designation; whereas AIU is recognized internationally and can offer all programs and degrees.