Rednu, I believe the team you remember was DIII Drew in Naismith. In season 28 their coach alex24057 went ballistic on the forums (I don't know why) and was banned. His team won the NT with a 27-8 record. In an ironic twist of fate, alblack56 took over Drew the following season.
I think my Rhode Island team from season 43 of Iba may qualify as the "worst" team ever to win a DI title. It really wasn't that bad of a team except for their 16-11 record entering the NT. The team had 1 Sr, 4 Jr, 5 So, a Freshman and a walk-on. Excluding the w/o, we had a 741 overall total. That team was part of the mighty A-10 that was extremely strong at that time. That season we sent 8 teams to the NT and 2 more to the PI. My team went 6-3 vs Top 25 teams and was an at-large selection as a 10 seed. We won 3 games against very good opponents and then faced the legendary lostmyth2 in the Elite 8. After beating him to advance to the Final Four, lm2 posted on the CC that since I beat him that I'd better win it all. I had no choice but to win the next two games and the title.