Issues of New World diffusion are extremely complex, and uniquely confusing. Mainstream scholarship has been extremely skeptical of the disparate theories and books in this area, while proponents of diffusion tend to introduce a host of wild claims based on unsupported material that tends to discredit the whole subject. One thing we can't do here is the settle the question, so, before entering the fray, it is worthwhile remembering that nothing short of smoking gun evidence is sufficient. And that evidence tends, on the one hand, to be lacking, suspicious in itself, or to be ambiguous to the point where nothing can be concluded from it. The answer is simple, information is tasteless, odorless, and can travel in small doses to have a large effect.
Men can climb in a boat and seed influences afar.
They do that everywhere else. But the New World is to be a puzzling exception to this. Thus the evidence could be nearly nothing. A good example is the lore, black hole, of debate over the famous Olmec heads, which look like men of African descent. After the smoke settles on the battlefield of this question, I can only say, I don't know, as I slip away from madmen.