Pete, you've made an excellent summary. If we were to use the true original definition of a fly, not only would it be constructed of natural materials, but it would only imitate insects. Therefore, even a streamer that's made of natural materials would not be considered a fly because it imitates a baitfish and not an insect.
FWIW, there's just too many patterns out there today that use some sort of synthetics to be ignored. My striper and bluefish boxes have several patterns that are constructed entirely of synthetics, and such flies would probably make Halford and Skues roll over in their respective graves. But that doesn't stop me from using them. And I have no problems with people who think otherwise. To each his own.