Did you believe Da Vinci Code as well? ;D
I've googled "India Once Ruled the Americas" and it is nothing but a laughable fairy tale! Only an untrained reader will buy his loose views.
The peoples of Americas couldn't have developed a completely different culture across the continents between the 15th and the 19th Centuries. Had Americas been populated by "Indian rejects", the languages spoken there would still be close to the Indian Languages. Once we're talking about a recent period, many aspects of the Asian culture would have remained to this day. They would be flagrant and obvious. This book is a fraud.
The Indus Valley Civilization dates back approximately to 5500 BCE. The Asian peoples crossed the Bering Strait from 23000 to 9000 BCE. Thus, it's not possible that India ever ruled the Americas.
Many words are alike, but they don't necessarily share a common root. Scholars have proposed that Japanese and Korean belong to the Turkic language family. They show some similarities, indeed. However, the earlier forms of any related languages must be closer than their modern forms, and that's not what happens when we compare Japanese and Mongolian, e.g. Their evolution shows different morphosyntactic patterns.
Once we can't know how Nahuatl evolved, it's not possible to realiably compare it to Sanskrit. Moreover, according to what I have read about the Aztec language and Tupi syntax, both are very different from Sanskrit's. Did the author even use phonology reconstruction?
DNA analyses suggest the indigenous peoples of Americas have Siberian roots.
If you like theories, see the new hypotheses based on more recent DNA studies which proposes that the indigenous peoples of America have Australian and Polynesian background. It also claims that Clovis wasn't the only paleoamerican culture.