The most likely reason is that a lot of black voters left the ballot blank in those counties in that race because there was no Democrat (only a Reform candidate).
Just using one of your examples, Bryant only got 48 votes more than Barbour did in Bolivar County. Keep in mind that Barbour only got 35.1% of the vote in Bolivar. It's a similar story in Coahoma, where Bryant only had 41 votes more than Barbour (who had 36.5% in that county).
This isn't actually particularly unusual behavior in the Black Belt either. In 2014's Senate race in neighboring Alabama, Jeff Sessions was uncontested, resulting in him getting 90%+ of the vote in nearly the entire Black Belt. However, when you include blank ballots, you notice how most of the Black Belt simply left their ballots blank:
According to the Atlas, Bryant's opponent was a Democrat, and looking at county vote totals, turnout doesn't seem to be particularly depressed in the majority-black counties.
Atlas listing Blackburn as a Democrat is an input error. The
Mississippi Secretary of State's certified candidate list for 2003 has Blackburn listed as a Reform candidate.
On your second point, turnout isn't mutually exclusive to people leaving their ballots blank in a particular race that doesn't feature the party they voted for. I can demonstrate that here, using 2003 Attorney General as a reference point for downballot voting (some voters leave the whole downballot blank):
Bolivar County votes for 2003 Governor: 11,387
Bolivar County votes for 2003 Attorney General: 9,570
Bolivar County votes for 2003 Auditor: 4,148
Coahoma County votes for 2003 Governor: 6,608
Coahoma County votes for 2003 Attorney General: 5,285
Coahoma County votes for 2003 Auditor: 2,620
Sunflower County votes for 2003 Governor: 7,154
Sunflower County votes for 2003 Attorney General: 7,041
Sunflower County votes for 2003 Auditor: 6,110
Jasper County votes for 2003 Governor: 6,534
Jasper County votes for 2003 Attorney General: 6,475
Jasper County votes for 2003 Auditor: 5,707
Basically, many Dem voters (particularly black Dems) simply didn't bother to vote in the Auditor's race, even if they did vote in other downballot races.
