Reality of 99% of non-accredited programs is that they cannot possibly meet the basic requirements of real accreditation. They do not have the requisite faculty education, library, campus facilities, and academic strength of content to reach it.
There is NO COMPROMISE of the biblical/spiritual standards of a school to become accredited - matter of fact, the accrediting team for a school like Maranatha Baptist University was intentional comprised of leaders from other Christian universities. The old "myths" that a school has to give up Bible classes, chapel, dress standards, separation from the world, et al to be secularly accredited were long-ago dispelled. There is no "jurisdiction" or "control" of an agency over the schools. They are the bugaboo's that schools who offer shoddy sub-standard programs give to dupe their followers into thinking they are just as good or better than an accredited school.
The Italian word for that nonsense is "bologna".