That's because it basically was done live, as far as I know and can tell. Ben was at my school to record the Ramblers on "Army" and he was using a pretty basic setup, sort of like a high-end version of the background mics you'd find at most college aca concerts. They just kept doing takes until they had something they liked, no punching in fixes or anything. And I think there was almost no post-production. Frankly, I'm impressed that a lot of it is as good as it is. It's damned hard to be that exposed without the Pro Tools safety net.
The lone exception might be "Selfless, Cold and Composed" which sounds to me like the version that group recorded on their own. Their YouTube upload sounds exactly like the track on Folds' disc: http://www.youtube.com/watch?v=kB9hjYLkTMg
The buzz I read, largely here at RARB, also implied that this was kind of a low-budget thing for them. I don't think they had the financial backing to send everyone and everything out to our favorite mavens for star treatment. As it was, Ben was conscripted into doing two of his own tracks just to get his label to agree to the album. Unsurprisingly, they're the only ones with any semblance of production—of course, he also did all the vocals himself, so it's not like he had a choice.
Hope that helps answer some questions; if I'm misinformed on any of this, I'm sure someone more knowledgeable will set us both straight.