What you are describing is exactly what GP complained about: "state as something distinct from both the UI and the data source".
React can be 100% stateless, functional, and have the state live somewhere else. You just need to apply the same limitations as your model: components should be simple and not store data in themselves.
This is why people came up with things like Flux/Redux/Reducers/Immutability, to handle this in a standardized way, but nothing is necessary.