Yes, I have seen others advocate the "as nature intended" orientation for sticking the leather down - even one or two bookbinders I know strop their paring knives that way.
The primary reason for the flesh-side up orientation is that the fibrous structure of the inside surface is slightly better at holding the sharpening/polishing compound than the often rather shiny hair side of a piece of leather. Hide/calf-skin should be OK to use hair-side up because it typically has a somewhat duller and more absorbent outer surface in its tanned state than the outer surface of a piece of goatskin, which often has a fairly high polish when it leaves the tannery. On the other hand, the fibrous structure of the flesh side of goatskin is usually of a denser "weave" than that of the flesh side of a piece of hide/calf, so it provides a surface that is a good compromise, in my view, between absorbency/compound-retention on the one hand and smoothness on the other.
Whatever leather you use you don't want it to be too thick (0.5mm or below is about right), otherwise the knife may sink into the leather too much and its bevels/angles get rounded off when you want them to remain sharp.
Faith, there are many ways of achieving a sharp cutting tool and there's no agreement on which way is best, even for the same kind of cutting tool. A couple of general principles are that the blunter your cutting tool is to start with, the coarser the cutting material can and should be at first, and as your edge starts to get sharper you use progressively finer grades of whatever choice of things you're sharpening with, e.g. diamond stone, silicone carbide paper, water stone, arkansas stone, cutting/polishing compounds. The other principle, for novice sharpeners at any rate, is to keep a keen eye on the edge you're working on to make sure your sharpening is progressing properly; for tools as small as gravers this means using magnification. But you'll be used to that already.
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