YEah, sinew holds points on very securely. In fact, based on my experience, sinew is superior to just about any modern string or thread, due to the fact that it shrinks as it dries. It also becomes very thin. So thin that it leaves no abrupt surface to slow penetration. Use some pine sap glue to secure the point, then wrap over it with sinew and you will be amazed at just how strong that primitive glue and binding really is. I've shot arrows like that through deer and the stone point is still mounted as though I had used modern epoxy.
I don't like or use fake sinew for wrapping stone points onto any of my arrows...it just doesn't hold nearly as well as real sinew....