Hard to believe a I-A power would play a I-AA school when there are what, 3 times as many basketball schools in I-A than there are football schools? Even in football it’s pretty rare, and grounds for being blasted nationally and laughed at when you can’t make the BCS top 2 as a result.
Schedules are done years in advance, and Div II schools are done for a number of reasons. Some of them are actually good programs. And Div II schools can and do beat Div I teams - Chaminade is a good example.
Actually UAPB is above a Division II school. It is Division I. They could play in the NCAA tournament if they win their conference tournament. They are in a conference with several other historically black institutions (Grambling, Southern University, etc).