^The could wouldn't really make a difference, since the action in the past involved the Chinese, Russians, and David Cameron. The problem is that Obama's "...one of the meetings" isn't well phrased. If he had said "any of the meetings," it would have suited the "them" more.
But as an example, take the statement "I had an order of nachos with some people today. I didn't learn any of their names, though." The question "Do you like them?" is automatically assumed to be about the people, rather than the nachos. Like octothorp said, the most recent appropriate noun.
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