Ancient Mayans in Ancient USA? Big Debate

At the demise of the Mayan civilization, did the middle classes and commoners head north and form new cities in what is now the USA?

NB: Examiner.com content comes from thousands of writers who are self-motivated independent contributors.

People of One Fire researchers have been aware since 2010 that when the English arrived in the Southeast, there were numerous Native American towns named Itsate in Tennessee, Georgia, South Carolina and western North Carolina. They were also aware that both the Itza Mayas of Central America and the Hitchiti Creeks of the Southeast actually called themselves Itsate . . . and pronounced the word the same way.  The Itsate Creeks used many Maya and Totonac words. Their architecture was identical to that of Maya commoners. The pottery at Ocmulgee National Monument (c 900 AD) in central Georgia is virtually identical to the Maya Plain Red pottery made by Maya Commoners.  However, for archaeologists to be convinced that some Mayas immigrated to the Southeast, an archaeological site was needed that clearly was typical of Mesoamerica, but not of the United States.

I think perhaps both sides are correct. The idea was certainly accepted 150 years ago, with the main impetus coming from the similarity of place names. Modern archaeology says there is no evidence of upper-class Mayans in the USA, therefore they never made it that far north. The article writer, Richard Thornton, says it was only the middle and lower classes that migrated. And it looks like a lot hinges on the aspect of when.
There have been some damning articles, but the platform he chose, Examiner.com (yes it is a content farm, but not as bad as most). And disregarded the great deal of research and collaboration Thornton has conducted.