The mistake is in not realizing that the air that the propeller acts upon is
unchanged regardless of the speed of the conveyor belt. Therefore, the
propeller will be able to pull the airframe forward on the conveyor
regardless of how fast the conveyor moves, because it is putting a force on
the airframe relative to the air, not relative to the conveyor belt.

The same thing would happen if you attached a rope to the nose of the
airplane and stood on the ground ahead of the conveyor so that you were not
standing on the moving belt. Start the conveyor and the airplane stands
still while the wheels spin with the conveyor belt. Now pull on the rope
and you can move the airplane forward even though the conveyor is moving
backwards and the wheels are spinning like crazy.

The mistake I made in comparing it to a seaplane on a river is that the
floats are attached to the airframe - where they go, the plane goes. No so
with wheels. Wheel rotational speed has nothing to do with how fast the
airframe moves in this scenario.

BDS