First - public schools accept private school students and private school students accept public school students all the time. The Ivy Leagues, MIT, UChicago, Stanford, Duke, Baylor, etc are all private institutions, yet every year thousands of their alumni enroll in public institutions such as Berkeley, UNC, Virginia, Arizona State, etc. It really depends on the accepting school whether to accept/recognize particular institutions or not.
I think that is at the heart of the matter here is accreditation.
UAT is accredited by ACICS (Accrediting Council for Independent Colleges and Schools)
http://www.acics.org/
. According to the Department of Education, ACICS is responsible for "the accreditation of private postsecondary institutions offering certificates or diplomas and postsecondary institutions offering associate's, bachelor's, or master's degrees in programs that are designed to train and educate persons for careers or professions where business applications or doctrines, supervisory or management techniques, professional or paraprofessional applications, and other business-related applications support or constitute the career."
http://www.ed.gov/admins/finaid/accred/accreditation_pg7.html
UAT seems to be "professionally" accredited in business, but not accredited by a regional accrediting agency. For Arizona, the Dept of Education recognize the North Central Association of Colleges and Schools, The Higher Learning Commission for "the accreditation of degree-granting institutions of higher education in Arizona, Arkansas, Colorado, Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska, New Mexico, North Dakota, Ohio, Oklahoma, South Dakota, West Virginia, Wisconsin, Wyoming, including schools of the Navajo Nation and the accreditation of such programs offered via distance education within these institutions."
www.ncahigherlearningcommission.org
This may be why ASU was unwilling to accept classes from UAT - not a public/private issue, but more an issue of proper accreditation. Midwestern University is also accredited by the North Central Association of Colleges and Schools.
Just because MWU/AZCOM is private doesn't mean it will or it won't recoginize classes from UAT. Your best bet is to call the office of admission at AZCOM and see what the situation is. You don't want to spend money in the application process and then find out you don't fulfill the "90 semester hours" requirement because the school decided not to recognize work done in a non-regional accredited institution.
This concept of regional accreditation and specialize accreditation body is quite confusing. Welcome to the world of education and federalism. Again, I suggest you call the school and speak to a premed advisor at ASU.
Good luck in all future endeavors.
-Group_theory
PCOM 2007