The SEC has 4 teams with winning conference records.
There are 5 Teams with losing conference records that are bowl-eligible. These include non-conference wins over:
McNeese, Central Michigan, UL-Monroe, GA State, Akron, AL State, Samford, USF, FAU, Eastern Illinois, Troy, SE Missouri, North Texas and a few others. These 5 teams were a combined 1-4 vs. other P5 conference schools, each playing only 1. The only win came from UF's 3 point win over 5-7 FSU.
13 bowl eligible teams sounds great. But the details aren't quite as impressive.