I think what Jeff is picturing is the old Thing-O-Matic setup. There were two big problems with that setup that are solved with using the belt as a "z-axis" of sorts.
First, when the belt was used as the Y-axis in the Thing-O-Matic, it would be moving back and forth constantly, wearing on the belt very quickly. The way the Printrbelt and Blackbelt are set up, the belt only moves a tiny bit for each layer, and never moves backwards, making the belt wear negligible by comparison.
Second, when the part is ejected, the Thing-O-Matic would just run the print off the edge at high speed, which caused huge stress on the belt which, because of the first problem was already prone to wearing out very fast right on the one spot where the print was stuck, this lead to belts tearing after about a dozen prints. With these setups, the print gets unstuck from the belt one single layer line at a time, and the hot spot of the print constantly moves, to keep wear on the belt from getting concentrated in one place.

Just a few thoughts, I hope all of that made sense.