Actually, I just finished reading Thor's book.
When he brought up his theories, scientists poo-pooed it because there was no way that ancient Indians could have reached Polynesia. They had no ships.
So he set out to prove they could indeed have gotten there, which I believe he did quite conclusively.
He never said that his voyage would prove what happened, only what could have happened.
Have you read his later book about their explorations on Easter Island, Aku-Aku? The stories about their crawling into the family caves absolutely made my hair stand on end (I HATE low dark places.)
The thing is sort of lost in the hullabaloo is that Heyerdahl's theory of the settlement of Polynesia from South America was indeed proven wrong by DNA...
The problem is his voyage is far more exciting and interesting than DNA testing; a problem with science in general as the exciting stuff gets more general media attention.