Not entirely so. I dont recall exactly, but i think Teotihuacan actually lasted longer than that, and some Mayan dynasties lasted more or less the entire history of their civilization, or so I gather - someone else should either confirm or deny that (with varying degrees of independence and power, mind you, but that's still existing).
It also depends a bit upon how you view a civilization and continuity.The Chimu, for example, were probably direct descendants of the Moche who had preceded them hundreds of years, and many Mesoamerican kingdoms saw themselves as successors to preceding ones, especially the Teotihuacanos (an analogy that could be applied to several old world entities, as well)