"Selfbows" are made using a wide range of tools...from stone tools exclusively, to purchased tools such as bandsaws and beltsanders. In my opinion unbacked wood bows from billets should be considered selfbows even though typically a modern type tool such as a bandsaw is used for the splice. The majority of us use some form of modern tool in the building of a one piece selfbow. If billet bows were excluded from the selfbow category, you potentially exclude many people from participating due to their lack of access to quality full length staves.
I agree that "decorative" materials such as snake skins and thin barks (birch bark for instance) should be considered a selfbow still. The debate gains momentum when decussing from what point a glued material on the bows back crosses the line from "solely decorative", to adding some level of protection for the bow against breaking. A sinew backed bow adds protection as well as potential increased strength and performance, but is still considered a selfbow and is also an example of primitive construction. Some fish skins and rawhide most likely add some protection to the bow although not usually increased performance. With the almost unlimited range of potential backings, it could be a long winded debate as to where the line is drawn. Maybe the process involved in attaching the backing itself should be considered as a deciding factor between selfbow and backed bow. If the back of the bow is left in its natural shape with dips and uneven surfaces prior to applying the "plyable" backing, then it is still considered a selfbow. If the back of the bow is worked full length of the limbs to attain an even surface required for the gluing of a laminate, then it is considered a backed bow or laminated bow. I agree with Oldbow that perhaps the wording should be changed to "laminated bow" to help cut down on confusion.