That's what they meant by "in boat displaces its weight in water". While it's in the boat, the amount of water it displaces weighs as much as the bowling ball. While it's in the water, it displaces the volume of the bowling ball, and its weight doesn't matter. The ball is denser than water (since it sinks), so the amount of water it displaces based on its weight is bigger than the amount of water it based on its volume.
