1) A team not named Grambling or Southern manages to not win their division but is still good enough to receive an at-large bid.
2) Grambling or Southern don't win their division but has a team so good that they earn a bye in the FCS playoffs, thus not having a Thanksgiving weekend conflict.
The last SWAC team to participate in the I-AA playoffs was Jackson State in 1996 I believe. They were steamrolled by William & Mary 45-6 in the Round of 16.
Ivy/SWAC challenge in Week 1 would be a great idea -- bring on an 11th game!