For those who are still confused and have troubles realizing why rivers flow as they flow, I try explaining it in simple terms that any person without any education in physics might understand:
Try imagining the Earth is made only of water. It would still have the pretty same ellipsoidal shape as the true Earth has, with the exception that there would be no hills. The Earth surface would be equal to the sea level. Everywhere and constantly. Still, the water surface on the Equator would be miles further from the center of the Earth than the surface on the poles. Despite it, the water would not flow away from the equatorial bulge ("down the hill"). It would be in equilibrium all over the planet.
Now, if you took a bucket of water, raised it over the surface, and poured down a ramp, it would always flow down to the sea level, regardless of your position on the Earth, and regardless of the direction and the length of the ramp.
It is as simple as that. You do not need to have any deep knowledge about gravitational and centrifugal force, or about your distance from the center of the Earth.
In other words, as stated already several times here in the thread, here on Earth we do not measure the altitude by the distance from the Earth center. We measure it as the distance from the sea level (in given place). And rivers follow the same logic - they flow from places elevated above the sea level, down to the sea.