The land we now call Mexico was there long before there were people around to argue about what to call it.
And the people who occupied it for most of the last 12,000 years certainly had very different ideas about what any particular bit was called.
"Human sacrifice was common in many parts of Mesoamerica, so the rite was nothing new to the Aztecs when they arrived at the Valley of Mexico, nor was it something unique to pre-Columbian Mexico."