As far as I see it, you can make a primitive bow, and then you can make a primitive bow primitively. Steel, even steel hand tools, are not primitive. Neither wood iron. Maybe copper tools. Maybe. But you can still make a primitive bow and no one would know how it was made, its the same product. But to make a bow primitively, in my mind, you would have to do like the cavemen. Start from nothing. Go out and make a stone knife and hatchet, then find some fiber and make cord. Then fell a stave etc etc.
This is actually a goal I have for myself and something I am thinking of doing a youtube serious on. My goal is to go out and use nothing but nature for my bow. I have obsidian for tools, new mexico locust for staves, and yucca for fiber. That's about as primitive as it gets, and would expect no one sane to want to do it that way haha. Of course to help make it easier, I'm going to build the same primitive bow using non-primitive means first, and then try it the hard way.