The evidence for Polynesian contact is interesting but the Polynesian migrations were much later.  Sweet potatoes made it to the Cook Islands after about 1000 AD, although that does not mean that Polynesians weren't in South America before then.  There is also evidence of a South American genetic imprint on Easter Island.  The exact process of how South American genes got to Easter Island is a matter of speculation, but I'm guessing that there were some horny Polynesian seafarers a long way from home.    