>It'd be like claiming the different people that inhabit the same house over the span of 100 years are all the same people, because they're all humans. They're all people, and they all inhabited the house ('the people in that house'), but they in fact possess different unique identity.
If it was the same family or if they shared a few genetic markers that distinguished them from other peoples in the area... then you could say the same people had lived at ________ area.
If it was the same family or if they shared a few genetic markers that distinguished them from other peoples in the area... then you could say the same people had lived at ________ area.