The area around a major river being greener helps in no way the emergence of a river civilization.

What matters is that the river banks are fertile, the area has a good climate (especially a long growing season), domesticates were brought, and the area around is worse for sustenance.

Much to the contrary, the area around being better for sustenance probably makes it more difficult and unlikely for a civilization to emerge, as it allows people to freely escape taxation / corvée by just migrating away from such attempts.