The article also suggests some think it might just be the effect of their most recent common ancestor in Asia somewhere, and not from any kind of transplant.

The American continents are kind of hard to miss. After sailing east from tiny island to tiny island, it is kind of hard to believe that they didn’t run into the continents at some point while looking for new islands.

Maybe, maybe not. Easter island is one of the most isolated islands in the world and is also one of the easternmost islands in the Pacific. It's still a long way to go to get to South America from there. Maybe a few family units arrived and then forgot about boat building and navigation for a few generations because the islands land resources were so plentiful. I think something similar happened to native people on Tasmania - they took a boat to get there, but forgot how to build boats eventually and so were stuck on their island without the ability to go to mainland Australia.