They actually are. Depends on what you consider the river. If it is just the molecules of water, probably not. But if you look at the whole ecosystem of a river

They actually are. Depends on what you consider the river. If it is just the molecules of water, probably not. But if you look at the whole ecosystem of a river, you will be amazed. And in this situation with beavers building dams and changing the course, and everything doing its bit, yes, the river will do amazing things and will show to have a life of its own, just like the ant colony.