His only actual conviction was for providing alcohol to an underage person.
Supreme Court says there's passage of time, and also these are kind of minor issues. They tried to find ways to be deferential to the board, but they essentially overrule them. Generally, the facts and their credibility are not subject to review on appeal. The board made a finding that he lied to them, and it is essentially set aside.
So denial by the board can still be appealed, and the Supreme Court is concerned only with major issues. Note that over 2 years go by between his initial appeal and this remand. So even a favorable ruling can imply a significant postponement of one's career.
The scope of inquiry for bar admission can lead to abuses, but this is vanishingly rare.