There is no validity to such claim because it assumes a single reductionist linear development for human history (sometimes call as a neoevolutionary perspective). It basically suggest that, given enough time, New World societies were going to progress in the same way as their Old Word counterparts. Rather than being a sound theory to interpret history, the view of linear development ends up being a deterministic tautology without history or any room for idiosyncrasies. It is flaw because it takes any society around the world and locates it within a linear progression with hunter-gatherers on one end and European states as the ultimate end of history. So my question is, where is there room for contingency? Where is there room for human agency? Where is there room for diversity and multiple paths? Where is there room for the individuals actions of unique individuals that actually make history? Where is there room for the consequences of those actions that themselves bring about different outcomes? We see a great diversity in ancient societies because they took different paths, were entangled in different ways with their facticity, and chose (consciously or subconsciously) to incorporate those elements into their cultural networks differently, causing diverse intended and unintended consequences. We see diversity because there is no single path for human history.