The statement that modern humans (H. sapiens) became established in the same region as the last Neanderthals approximately 39,000–42,000 years ago suggests that there is a possibility of overlap between the two species. This means that Neanderthals and modern humans may have lived in the same region for up to approximately 2,000 years. However, the evidence does not conclusively indicate whether they interacted directly, competed, or coexisted without substantial contact.
The notion that modern humans killed off the last of the Neanderthals is a hypothesis rather than a definitive conclusion, as the reasons for Neanderthal extinction are still debated, including factors such as climate change, competition for resources, and interbreeding.
The claim that Neanderthals and modern humans could not have lived in the same region at the same time contradicts the evidence of their overlapping timeframes in that area. Therefore, the most plausible interpretation is that there may have been some period of coexistence, although the nature of their interactions remains uncertain.