Of course, the "river" is far to narrow for those big boats to be steered manually.
Sometimes, if they go around the bend a bit too fast, you can feel how the ship is pulled around on the rail.
If you ever saw one of the "Making of" films that were shown on TV around 1991, there is footage of the empty river and you can see the rail. It is the same system as with the smaller boats in "Jungle Cruise".
However, the Keelboats (and the Canoes, when they were still around) are steered by the CM aboard.
Marc