I've not done it yet myself, but my understanding is that you're essentially trying to create conditions similar to air layering, only you already have roots to work with.
The roots are draped over the rock, then moist soil pressed in over them so they have something to grow in, then it's all wrapped to hold the whole mess to the rock. You have to use the, "muck," as you call it because otherwise the soil won't hold in place on steeply angled or even vertical rock sides. As the roots grow they find their way into the crevices and pores of the rock, eventually adhering to it, and elongating down into the more traditional soil at the base of the rock. After the roots are set into the soil under the rock, the wrapping id removed and the old, "muck," can be washed away by watering or removed intentionally, revealing the roots underneath.
When done with slabs (again, haven't gotten there yet but it's on the list) the same thing is sometimes done if the slab is at a steep angle, or the there are no sides to hold the soil in.
This is my understanding from a little bit of research. I may be trying out both this year if I find the components that prompt it.