OK another thought experiment.
Imagine a large tank with a consistent artificial current flowing through it.
Now imagine a model boat placed in this stream, bow upstream.
You hold one finger against the center of the transom so the boat is stationary over ground.
With this model I thing it is pretty easy to see that keeping it perfectly balanced would be very hard. The bow will want to fall off very easily and quickly.
Probably a reiteration of what was said in the previous post, but hold the boat from a point in the center (where the boat's CE is located), and it should track very well. Boats pivot around a location just above their keels, not sterns.