This is a truly useful, socially responsible thread, and my thanks to all tho have contributed thus far.
Ray Mears does make me wonder sometimes. There he is, in the Canadian backwoods, travelling light and simple like the old voyageurs and Indians, and then suddenly he produces this whacking big auger from somewhere (possibly hidden with a load of other carpentry tools for making his traditional canoe the Indian way - pfft!) and he gouges this deep, wide hole right into the birch tree. And taps the hole with a spigot. It struck me at the time as crass.
Maybe the voyageurs - some of them, anyway - were crass and didn't care about the health of the trees, but I can't imagine Indians ever doing that. Neither can I imagine any Stone Age people doing more than making shallow cuts just into the cambium, or cutting a small branch as others here have described. They would have chosen a method that didn't need specialist tools and were willing to wait - they were rich in time, and didn't need industrial quantities.