I realized that my comments may have implied that the force argument is
wrong. But it is correct, while what I would call it indirect. My comment
about pre 8 year olds is just pointing out that the previous style of
reasoning is using forces, so that route would tend to be the first one that
comes to mind. But an expert will then use what first somes to mind and
with various backtracks eventually come to a good solution.
I am always confronting the problem that even some college students think
that submerged heavier things of the same volume push up the water more. So
I immediately divide buoyancy problems into 2 classes submerged and floating
with the consequent volume displacement. Unfortunately buoyancy is not well
taught in many physics classes. Students come into a college class even
from a HS physics class and have not been confronted with buoyancy. They
think the Helium in a balloon pushes it up. This is true of even
prospective engineers in a calculus based course who have taken a HS physics
course.
The red herring about the normal force is that you don't have to invoke it.
When the rock is going down after being submerged, there is no normal force,
but there is fluid resistance and the rock will be accelerating part of the
time. The volume argument is independent of the details of where the rock
is located in the water.