I assumed in the movie anyway that the Bulls were AAA since Robbins character was in fact called up to an MLB team. Whether it was AAA or not, its not really accurate to say "In exchange for helping Nuke reach the next rung of the minors."

In the movie, I don't know what level they were, but I would suspect AA since their bus was decent, and it is a good crossroads for players on their way up and down. Jumping from AA to the bigs isn't unheard of... Pitchers with good "stuff" still have it regardless of the quality of the opposition. So Robbins's character could have gone to AAA but instead went directly to the show.

In real life at the time, the Durham Bulls were a single-A affiliate of the Atlanta Braves. They are now a AAA affiliate of Tampa Bay.

Its a quibble on the article's wording to be sure to be sure, but I think its safe to say the Bulls organization had Crash Davis tutor Nuke not to bring him up one level, but to get him ready for the majors. I just thought it was a strange way to frame Crash's job given that Nuke was clearly a big leagues talent guy who in the movie actually made the Majors.

I might be wrong, but I think that in the first meeting of Crash and his new managers he questions why Durham bought out his AAA contract.