Fun fact, the only major football teams to play fewer FCS opponents than UT are the following: OSU 2 Colorado 2 UCLA 0 USC 0 Notre Dame 0
I realize those South Carolina losses don't technically count, I was just going with teams that are currently in the SEC. Missouri and Texas A&M are both undefeated vs FCS.
So, Citadel beat Arkansas in their first year in the SEC and South Carolina before they joined. Other than that, it looks like the two Mississippis already mentioned stand alone atop the conference wall of shame.