Publishing refers to how you handle the composition rights, e.g. the rights to the written song itself, not any particular recording of the song. Some artists, like Prince, own their own publishing and thus publish all of their own compositions. Many others wind up signing deals that give their labels a significant chunk of their publishing.
At present, composition rights still comprise the more lucrative of the two groups of rights inherent to any recording (the other rights being the Sound Recording rights, e.g. the "SR" rights or mechanical rights), because radio play generates royalties for the composer, not the performer, and public performances of the song likewise give the composer royalties (cover bands, jukeboxes, etc.).
The distinction that PSM is talking about really goes to whether the producer gets paid on the front end with a fee or on the back end with points. It'll be some combination of the two, but the exact mix varies. PSM has stated that his fee is never recoupable, which just means that he doesn't have to earn the equivalent of his fee in royalty points before he can be entitled to payment of any more royalties.
Example: say a producer has a $10,000 up-front fee, that is 100% recoupable, and gets 3% on the back end. He gets that $10,000 before the song gets released, but the song has to earn him the equivalent of that $10,000 at the 3% rate before any more payments are going to come his way. The label is "recouping" its initial investment. PSM is describing a deal where he gets paid $10k up front plus 3% on the back end, but that 3% starts coming his way immediately, no repayment to the label due first. That's to his great advantage, because a label is always going to try to f00k you in the a$$ with accounting to prevent having to pay back end royalties. By getting the cash up front, PSM is avoiding any funny numbers from the label.
Now, the artist is going to be the one paying PSM's fee, out of the artist's own slice of the pie. The lable is going to allocate the producer's fee, the studio fees, material fees, mastering fees, distribution fees, marketing fees, all of that to the artist's recoupment budget, meaning all of that sh1t has to get paid back before any more money goes to the artist.
Recording deals are a c0ck and a$$ thing, the label's c0ck, the artist's a$$...