I've never heard that perspective on barrel run out. It does seem like that is certainly a concern with minimal significance with modern scopes. I have heard the discussion about POI shift due to thermal expansion of the barrel. The idea is that if a barrel were truly straight it would extend in length when the barrel warmed up, and the outer diameter would increase and the inner diameter of the bore would constrict as the steel of the barrel expanded in all directions. In a real barrel the curve will be exacerbated by thermal expansion causing the POI deviation to vary with temperature. The physics of that makes sense, but the extent to which that exists practically is something I don't know. I just don't have any experience with it. The excellent point made above about the number of Accuracy International rifles that shoot great without this timing seems to illustrate the practical scale of this affect.