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Being "naturally formed" isn't a requirement to be a river. Being gravity fed and naturally flowing is. A canal doesn't have significant flow.

But would you really call this concrete structure you see in the picture a river?

If the LA River is any historical precedent, yes.

If the LA River can be a river, why not?

The flow of water was there before the concrete constructions were made, I guess?

Not necessarily. It's common practice to built structure to control and redirect rivers around developments. That doesn't stop it from being a river.