I've always wondered about that theory, even as a child. It was obvious they didn't have sufficient evidence. It just didn't make sense to me that, if there were adverse environmental consequences to "overuse," then the population wouldn't just drop to a sustainable level and stabilize. It only takes about 25-50 people in a tribe to preclude inbreeding.
The local folklore recorded by anthropologist Thor Heyerdahl told of a two-tier society during the statue-building era, and how there were two rebellions (perhaps during times of privations of some sort) the second ending in the near-annihilation of "the long-ears" by "the short-ears". The location of the long-ears' fastness is still known, the digs there confirmed one element of the tale, and overall this is consistent with the overall history, prehistory, and folklore of the Polynesians throughout the Pacific, and for that matter, with humans in general.