Credit to u/baconydraco, one of the mods on r/cfb for researching this.
Apparently by NCAA rules, a win against an FCS team only counts if the opponent is using at least 90% of the 63 scholarship limit, which Deleware State did not.
This rule would have also made WMU ineligible (win vs. Wagner) and Buffalo ineligible (win vs. Colgate); however, UTSA would be eligible meaning they wouldn't need to go to teams that were 5-7 like in previous years.
Seems like its too late to put UTSA in the Independence Bowl (12/27), but it's interesting because FSU has the longest bowl streak. I wonder if ESPN catches wind of this if whenever they bring up the streak, they will say something like "FSU has the longest bowl streak, but not the longest streak of bowl eligibility".
Anyways, seems like a cool piece of trivia.