Well personally, I'm just opposed to the rigidity of the twelve tone system. Even though that satirical song is about atonality, the singer makes no distinction between atonality and the twelve tone method of Schoenberg. He's a Nashville Money Manager, not a musician, so he probably doesn't even know the difference between the two.
To her credit, Fine resisted the twelve tone technique her entire career, and that's probably why Botstein decided to perform her work. If I know his taste in music, he's probably performing a piece from her tonal period. I think pretty much everyone agrees that the triadic tonality that ended with Wagner was pretty much exhausted. Schoenberg had to happen at some point, just as an experiment in a different direction, but Imho, and Fine's apparently, it was a failed experiment. Even Stravinsky's Piano Concerto resulted in an almost laughably distorted version of his music, as he struggled to maintain a part of his identity within the strictures of the twelve tone system. That period left him regretting his decision, and wishing he could go back to the tradition of being a "Town Musician", who just composed music for events occurring in his 'town'.
Even Gunther Schuller in that essay I quoted the last time we spoke about this said "We've emptied out the concert halls", there has to be a compromise between the twelve-tone system and tonality. As Fine describes her later period as mutating tonality, tempered atonality, and NOT composing by avoidance, she found the necessary 'compromise' Schuller spoke of.