The way he spoke was mistaken, but only by calling them Mexicans. Mayans were here around 900 AD.
Aztecs were here much earlier than the US was established as a country of itself. But then again, It depends on what you call a country. Its not as if the aztecs knew the process of actually putting themselves on a map.
http://en.wikipedia.org/wiki/Aztec#History
"The Nahua peoples began to migrate into Mesoamerica from northern Mexico in the 6th century. They populated central Mexico dislocating speakers of Oto-Manguean languages as they spread their political influence south. As the former nomadic hunter-gatherer peoples mixed with the complex civilizations of Mesoamerica, adopting religious and cultural practices the foundation for later Aztec culture was laid. During the Postclassic period they rose to power at such sites as Tula, Hidalgo. In the 12th century the Nahua power center was in Azcapotzalco, from where the Tepanecs dominated the valley of Mexico. Around this time the Mexica tribe arrived in central Mexico.
The true origin of the Mexicas is uncertain. According to their legends, the Mexica tribe place of origin was Aztlán. It is generally thought that Aztlán was somewhere to the north of the Valley of Mexico; some experts have placed it as far north as Southwestern United States.
Based on these codices as well as other histories, it appears that the Mexicas arrived at Chapultepec in or around the year 1248.[11]"