Why does layer-by-layer learning work?

The weights, W,  in the bottom level RBM define p(v|h) and they also, indirectly, define p(h). So we can express the RBM model as

conditional probability

joint probability

index over all hidden vectors

If we leave p(v|h) alone and build a better model of p(h), we will improve p(v). We need a better model of the posterior hidden vectors produced by applying W to the data.