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The case of the otters in the Aleutians seems to show that nature is not in balance, by any meaningful definition of the term.
At any given moment there is a network of different species feeding on each other. If this system is in balance then changes to the system should result in further changes which bring the system back into balance. The feedback loops should work to smooth changes in the system.
Instead, what you describe is a system that is not at all in balance. A change to the system results in a catastrophic feedback loop which forces ever greater changes throughout the network.
Any system is going to be have a tipping point where balance cannot be maintained, but the specific case you cite seems to be inherently out-of-balance.
If we apply the same reasoning to climate change there is one school of though which says that the Earth's atmosphere is in balance. Our increased emissions will result in feedback that will bring the system back into line with our historical experience. The other school of though would be that the atmosphere is not in balance and changes we make may result in feedback that will exacerbate those changes.