Heyerdahl was trying to prove that people sailed WEST from South America to settle the Polynesian Islands.
It's quite possible some of the immigration from Asia to the Americas was by boat, but most likely in a series of short trips along the coast.
The problem is with the Ice Age ending the coastlines they were moving down are now under quite a bit of water. Hard to do underwater archaeology for that sort of thing.
Yes, you're right, Heyerdahl was trying to link Western Hemisphere to Polynedian migration. But what I thought was interesting (I just saw the Kon-Tiki documentary a couple months ago) was how primitive his boat was, and it made it on such a long voyage.
A primitive vessel COULD have made it from Old World to New, as well. There is no PROOF or EVIDENCE, but the possibility remains. Early mankind may have been more mobile than we give them credit.