Back in 2010, I had a chat with Nick Patterson (one of the authors on that Nature paper) about the admixture problem. At the time, he was looking for an efficient algorithm for reconstructing ancestral trees subject to admixture. What he didn't realize at the time was that he was trying to solve a special case of Steiner Tree!
The Nature article states "some Amazonian Native Americans descend partly from a Native American founding population that carried ancestry more closely related to indigenous Australians, New Guineans and Andaman Islanders than to any present-day Eurasians or Native Americans. This signature is not present to the same extent, or at all, in present-day Northern and Central Americans or in a ~12,600-year-old Clovis-associated genome, suggesting a more diverse set of founding populations of the Americas than previously accepted." That's basically saying "mainstream academia has been wrong to date on an issue as basic as how and when people reached the Americas". There was, however, prior evidence:
Research by Ludwik and Hanka Herschfeld during World War I found that the frequencies of blood groups A,B and O differed greatly from region to region. The "O" blood type (usually resulting from the absence of both A and B alleles) is very common around the world, with a rate of 63% in all human populations. Type "O" is the primary blood type among the indigenous populations of the Americas, in-particular within Central and South America populations, with a frequency of nearly 100%. In indigenous North American populations the frequency of type "A" ranges from 16% to 82%. This suggests again that the initial Amerindians evolved from an isolated population with a minimal number of individuals.
I have been studying traditional navigation techniques of the pacific ocean over the last year or so and visiting museums across the world with surviving traditional and reconstructed craft. After learning the amazing variety of techniques used for navigation (celestial and otherwise) and the innovative food preservation and water collection techniques in recorded use for long sea voyages, I really don't doubt the ability of people to have crossed the Pacific in early craft.
All of the following are "right even if in reverse": Columbus started from the Caribbean and discovered Spain in the late 1400s; the Mormons left Utah due to persecution and relocated to the Midwest; Australians convicts in the early 1800s were transported to Britain to work and live in penal colonies; millions of free people were sold into slavery in the Americas and shipped to Africa to work; and the Mississippi flows from Louisiana to Minnesota.
Heyerdahl believed there were cultural similarities between pre-Columbian civilizations of the Andes and Polynesians because the South Americans "colonized the then-uninhabited Polynesian islands as far north as Hawaii, as far south as New Zealand, as far east as Easter Island, and as far west as Samoa and Tonga around 500 AD". (Quoting Wikipedia.) He also believed the current Polynesian population came to the islands centuries later by first going to the Pacific Northwest of the Americas and then to Hawaii before going to the rest of the Pacific.
Then maybe I should have said "the Kon-Tiki expedition was relevant even if not exactly in the way we expected". Thor Heyerdahl has proven it is possible to cross this distance by using only the materials and technologies available to those people at the time, that there were no technical reasons to prevent them from having done so.